The only real success I've had with him is tank support with a couple basic rules:

1. You need chalice, mana pool, armor/resists, and aura support.
2. No AP. Don't even bother with it.

The armor/resists maximizes your survivability with you're ult's healing more than going pure AP. Frozen heart is usually a great item because you get mana, armor, and a support aura all in one. The only reason to ever get AP is as part of an abyssal scepter for more resists and debuff aura.

I really don't get why everyone is so crazy about getting Rylai's for him. One of your spells already slows, and another flat out roots an area of effect. If you can't get the job done with that, then adding another slow onto your ult probably isn't going to make that much a difference. It's just a big huge waste getting Rylai's for a caster who already has a ranged slow, let alone a slow and a root.

The damage bonus from his E is really making everyone build him all wrong. He is NOT a nuker. There are over half a dozen casters who do that job much, much better. Deathfire is not going to "pwn" with that bonus more than a pure AP caster would.

Honestly, Swain plays more like a CC version of Mordekaiser with a mana bar than any burst mage.

Regardless of how "useless" he has been deemed as a caster, that is the role he fills. I have played 6 games with him, 5 of which are convincing wins. His ap ratios are not good and there is no denying that but it is his overall spell combo that contains the bulk of his damage.

First my items
Doran's Ring = One hp pot(this needs to last until lvl 6 when u can just ult heal yourself)
Sorcerer's boots
Rylais(only grab the tome and wand)
Tear of the Godess
FInish Rylais
Finish Arcangel Staff

These are the core items that any serious ap swain should be using. After words zhonya's, void staff, abbysal scepter, banshies or frozen heart are all optional.

The reason DFG is not used is because of the fact that it doesnt add enough dmg to his spell combo to be significant, and the mana regen is not enough to sustain his ult and spells for near long enough. Arcangels in prefect for sustaining his ult (as long as u kill minions intermittently) Rylais adds a slow to his ult and E.

I have enjoyed this champ more than any other before it. Perhaps its just my play style, but I can easily carry a team mid game. His role is unfortunately downgraded to CC support/carrykiller later game because his dmg is not enough to bring down beefy tanks.

I like this for a core
Doran's Shield + Pot
Sorc Boots
Deathfire Grasp

usually end build looks something like this
Deathfire Grasp
Sorc Boots
Rylai's Crystal Scepter
Archangel's Staff
Spirit Visage
Randuin's Omen/Banshee's Veil (depending on enemy comp)

Personally I have just fallen in love with:
- Rod of Ages
- Sorc Shoes
* Tear of the Goddess after this whenever you stop being capable of getting Golem for whatever reason.
- Zhonya's Ring
- Quicksilver Sash
- Abyssal Scepter / Guardian Angel
- Archangel's Staff

I really rely on QSS, W, R into Zhonya's active in the middle of a fight if I get hit by a stun or if I'm low on health.

Amplifying Tome ->
Sorc Shoes ->
Rylais Scepter ->
Will of Ancients (The 15% steal works well with your ult) ->
Abyssal Scepter ->
Zhonyas ->
Archangels.

If they have one person who is carrying the team and they have 3k+ health, ill grab a deathfire grasp instead of either the will of ancients or Abyssal scepter.

now I understand why people keep crying about his mana management. ppl need moer mana regen in their builds anyway.
my build:

Meki pendant
(archangel staff if im getting fed)
tears of mana
boots
blasting wand
archangel
sorc boots (im doin this cuz u dont relly ahve much AP to penetrate before u have AA)
(If im doing well stacks)
void staff/abysall scepter (depending on their team)
needlessly rod
building Rylais in this order: giant beld, blast wand, lil book

and this is how far i get, depending on how the game went i stack needlessly or get some utility from zonya/DFG or build a bit tanky or GA

Why not build Swain hybrid AP and AD. Torment increases the damage of all of his attacks, not only abilities, so maybe Rageblade, Nashor's Tooth, and Hextech Gunblade would be a good idea on him.