Once you land in Lordran you should have 2,000+ souls (thanks to the Asylum Demon) to allow you to level up a bit. Put 2 points into INT straight away to up your attack power.
With a bit of gentle grinding in the Undead Burg (prior to the Taurus Demon) you should get enough souls together to level to about SL12. If you are comfortable with the game you should be able to put all of these into INT (giving you an INT of 24), if not maybe beef up your VIT and/or END first.
1. Getting a Magic Weapon
Get a Longsword/ Shortsword/ Battle Axe (whichever suits your style better, although the Longsword works out best for upgrades in the long run but at this stage it’s probably best to suit yourself) which you should have gotten from one of the Undead Soldiers in the Undead Burg. If you opt for the Long Sword you'll need to up your STR by 1 and by 3 if you choose the Battle Axe.
Buy a Heater Shield from the Undead Merchant in the Undead Burg. This gives 100% physical protection which is essential.
Defeat the Taurus Demon and continue onto Undead Parish. With the souls you amass here get Blacksmith Andre to upgrade your weapon to +5 using the Titanite Shards he sells (the Undead Knights also drop these occasionally)
Head to the New Londo Ruins and purchase an additional Soul Arrow from Rickert. Open the gate to the Valley of Drakes (with the Master Key) and continue across the bridge and into the cave opposite. Run past the 3 club-wielding enemies and descend several ladders. On the lowest level you’ll find a chest containing the Crimson Set of armour (this is a great set of armour for Magic Builds). Equip it all bar the gloves.
This awful place is Blighttown. Keep going left (face the front of the chest which gave you the Crimson Set, left from there) until you come to a waterwheel. Jump onto a moving platform and descend to the ramp and jump off. Follow the land left and you’ll come to a tunnel on your left with a bonfire. Rest here then carry on, fighting past many more wasps and fire-breathing creatures, keeping to the left until you see a large tree trunk. You’ll find some Giant Leeches there, kill them and continue on around to the left where you will find a whole cave full of leeches. These enemies drop Green Titanite Shards (as well as Large Titanite Shards) which are essential to upgrading Magic Weapons. Here you will need to farm them until you have 10 green shards (when they drop green ones they drop 5 at a time so 2 drops is all you need).
Return to the New Londo Ruins by going up the waterwheel and all the ladders again. Get Rickert to upgrade your weapon of choice with the Green Titanite to become a Magic weapon. This scales with your INT stat so every time you increase it you will not only be increasing your spell power but your melee ability too. You should have enough souls and titanite to create a +5 Magic weapon. Buy Heavy Soul Arrow for 4,000 souls if you have them.
2. Getting some spells
Return to the Undead Burg and continue on to the Undead Parish.
At the top of the church you will find a knight in golden armour ( Lautrec of Carim), free him (with the Mystery Key) then kill him as the ring he drops ( Ring of Favour and Protection) is essential.
After some levelling here you should look something like thisaround SL25.
Make sure you activate the elevator to the left of the altar as you face it. Just step inside and roll out really fast, in order to activate it without having to do a double trip.
Near the lever that opens the portcullis outside the church you should find the Basement Key. With this return to the bridge with the dragon and on the far side there will be a door you can open (on the left). This brings you down to the lower section of the Undead Burg. The path up leads to a shortcut back to the main Undead Burg – use this to go to the Undead Merchant and buy the Residence Key.
Return to your shortcut and the path down leads to a town square with a bonfire in it. Kill the 3 dogs then go to the right and the right again (facing the opposite direction to which you came in). One of the doors will open with the Residence Key (you’ll hear someone crying for help behind it). Roll through the barrels protecting the prisoner to free him.
Go back to Firelink Shrine and Griggs of Vinheim (the freed prisoner) will now appear there. He sells some more potent spells. You should be aiming to get Great Soul Arrow and Great Heavy Soul Arrow.
3. Getting even better spells
Return to the church and fight the Bell Gargoyles on the roof and ring the bell. Next you will need to kill Quelaag to ring the other bell. She can be found back in the swamp of Blighttown. Return there via the gate in New Londo Ruins and the bridge across the Valley of Drakes.
From the bonfire at the side of the swamp head straight across the swamp via the small islands to avoid poisoning. When across head right hugging the left hand wall. You’ll come to an incline covered in webs. Head up there and you will see an opening (be wary of rousing the 3 Infected Barbarians to the right) continue inside to find Quelaag. Having killed Quelaag ring the bell behind her which will open up Sen’s Fortress.
You should have a few spare souls to level up and should be aiming to look something like this at around SL35.
Return to Firelink Shrine, take the elevator to the Undead Parish and when you come out go straight through the door ahead and continue straight until you get to the outbuilding with Andre the blacksmith downstairs. Rest and go out along the path beside the bonfire to get to Sen’s Fortress.
(Whilst in Sen’s Fortress you should pick up the Covetous Gold Serpent ring. When you arrive at the second door with a boulder rolling past (just after the arrow trap that shoots from behind), allow 5-6 boulders to go past, then ascend the stairs and redirect the boulders to fall into open space. Once that is down descend to the bottom of the stairs you came up from (careful of the serpent mage). At the end of the stairs will be a pit that should now be full of boulders, and a hole on the opposite wall. Beyond is a room with the ring which greatly increases your Item Discovery.)
You will eventually get to a room where the boulders are coming in from the roof – use the turntable to change the direction of the boulders once anti-clockwise. Wait until one boulder has gone down and change it again as you will be following the path the boulder just went down. When you get to the bottom you will see a new hole in the wall, go through and you will see some hanging cages. In one is Big Hat Logan in another a Soul of a Hero (which gives you 10,000 souls). Both can be opened with the Master Key.
Once freed Logan appears back at the Firelink Shrine. Go there and purchase the Homing Soul Mass. This is an excellent spell against most bosses. You should try to get your INT up to 36 asap so you can use the Soul Spear he sells.
4. The Crown of Dusk
By now you should also be more than powerful enough to take on Havel who is located behind the locked door in the tower that leads to the Taurus Demon. He drops Havel’s Ring which greatly increases your Equip Burden letting you wear heavy armour. Also he is guarding a shortcut to the Darkroot Basin which contains as essential item for all magic builds – the Crown of Dusk. To get this go out the door behind Havel and to the left you will see a 7 headed sea serpent known as the Hydra. This can be a perplexing battle for a magic build as range attacks are pretty useless (as they target the body rather than the heads of the Hydra). The only solution is to get in close to force it to use its heads in a lunge attack which can be dodged leaving the beached head open to melee attacks.
Once the Hydra is defeated quit and reload the game. Continue around the left hand side of the lake and you will encounter a Golden Crystal Golem. Defeating him releases Dusk of Oolacile. Having talked to her and said “Yes” go back to the front of the lake where you fought the Hydra and next to a boulder will be her summon sign. You need to summon her once before continuing. Now go to the back of the lake where you first found the Golden Crystal Golem where you will find her belongings suddenly have appeared including the Crown of Dusk which provides 20% extra damage to spells.
Also this will allow you to summon Dusk on the near shore of the lake where she sells some support spells. Of which Cast Light is essential for the Tomb of Giants and Repair can come in very handy also. The other spells are probably only useful in PVP.
5. Bellowing Dragoncrest Ring
Now you are a fairly battle ready magic user it may be a good time to explore some areas you may have missed like lower Undead Burg (where you rescued Griggs), The Depths (Once you kill the Capra Demon in Undead Burg) and Darkroot Garden (out past Andre the blacksmith) and get some souls together.
Using these souls I would recommend buying the Crest of Artorias first. This opens up the sealed entrance in the Darkroot Garden which leads to an area which is great for soul farming. Before entering the door destroy the wall to the left of the entrance to reveal a bonfire, rest here before going through. Inside you will be attacked by various bandits who are worth a sizeable amount of souls. They respawn so keep returning to the bonfire nearby and you should be able to pick up 7,000+ souls per foray beyond the door.
When you breach 20,000 souls return to the Firelink Shrine to purchase the Bellowing Dragoncrest ring which provides 20% extra damage to spells. Coupled with the Crown of Dusk you can do some serious damage.
You should be aiming to look something like this about SL45
6. Further Improvements
Go back to the Asylum (using the instructions here) to get the Crest Shield. This has very high Magic Defence and you'll need it as both the Crown of Dusk and the Bellowing Dragon Crest Ring significantly reduce your Magic Defence.
Returning to the Darkroot Garden, go through the door and keep going left through the small stone building, down some stairs and into another wooded area. Attack one of the small Mushroom Men and they will flee leading you to 3 larger Mushroom Men who can be tough opponents if underestimated. Defeat these and in the pool of water there is a chest with the Enchanted Ember in. Rickert in the New Londo Ruins can use this to make an enchanted weapon. However you will need Blue Titanite for this which is quite rare. There is some in the Great Hollow if you wish to explore there but the only farmable sources are Crystal Golems just before the Hydra boss in Darkroot Garden and Blue Crystal Golems in the Duke’s Archive.
To get there you will need to have defeated the boss in Sen’s Fortress, gone on to Anor Londo and defeated the bosses there too. Speaking to Guinevere (up the lift after Ornstein & Smough) and receiving the Lord Vessel opens up several previously locked areas including the Duke’s Archive.
Using the Lord Vessel at the bonfire warp to the Anor Londo bonfire. From here go left and continue on up the path beyond the guard building to find the Duke’s Archive. Here you will eventually find Big Hat Logan imprisoned (again!). You will eventually find the Archive Tower Giant Cell Key to release him after moving one of the bookcases with a lever. Upon releasing him quit and reload the game and you will find him in one of the library rooms behind the bookcase you moved. Here he will sell you crystal enhanced spells of which the Crystal Homing Soul Mass is essential.
In the other library room you will find a level which lowers some stairs. This will lead you out into a garden area full of Blue Crystal Golems who drop Blue Titanite Chunks. Equip the Covetous Gold Serpent ring to improve the drop rate and farm away (returning to the bonfire up the stairs to make them respawn) until you have 10.
To get a Blue Titanite Slab you will need to go out of the garden into the Crystal Cave. Keep following the path until it appears you come to a dead end. You will see snowflake-like crystals falling and landing on an invisible walkway, follow this across to terra firma and fight the Blue Crystal Golem there. Continue on left along this crystal land mass and you will begin sliding, when you stop you will be able to see another invisible walkway. Drop down onto this and immediately turn around to see a cave with 2 Crystal Lizards inside. Continue out the other side of the cave and you will find an infuriatingly twisty invisible walkway. Take it slowly here and look out for the snowflakes. At the end is the Blue Titanite Slab.
Continue on through the Crystal Caves to find the boss Seath the Scaleless. If you destroy the tip of his tail he will drop the Moonlight Greatsword which scales with INT and is worth considering for any magic build (it does require 16 STR to wield though). I’d strongly recommend summoning some allies if you wish to get the sword as you will need the distraction to get at the tail.
With the boss dead return to Logan. Buy everything he sells. When he has no more to sell he will start gibbering on and get angry with you. Quit and reload the game and he will have vanished but has left his robes and catalyst behind in a chest. His Sage Robe offers excellent lightweight protection at +5 (level up using Twinkling Titanite)
To get the most from Logan’s Catalyst (and its S INT scaling) you will need a INT stat of 41+ (NB beyond INT of 45 you will begin to see diminishing returns see table here for more details).
Return to Rickert to enhance your weapon.
At around SL 50 you should look something like this.
With those stats and your current arsenal the rest of the game should be quite manageable.