Not Updated For Current Season
Prevent Swain to be played as another headshot-teamflamer-******* champion and make him useful for the team (an ap - heavy one though), while still being durable and somewhat threatening.
Runes & Masteries
As your first items grab a Doran's Ring and a Health Potion. Doran's is a very gold-efficient and well rounded starting item for most mana-based casters. I get the health potion because with your passive and thoughtful use of spells you won't have to worry about being oom. It also may allow you to be that one inch more risky you need to get that kill.
Go Top/Bot, best against a squishy (clairvoyance, laneswap). Swaine is not a good option for mid lane because neither is he really good at farming nor does he need all that much gold to shine (and in comparison to typical mid-champions I find his results to be a little let down if he does). On the other hand Swains passive and his ultimate make him a really durable laning character. Also his harrassing abilities could help a generally weak laning character like Tryndamere to farm more effective.
Even though I found it most nice to have someone with high burst potential laning with me (Mundo for example works great), as you mainly go for dot and therefore can support your partner in getting kills.
Grab some kills in early-game. Later on dot, slow & snare enemies, so your mates are able to build up. Clairvoyance for awesome mapcontrol, Flash for nifty maneuvers.
Don't try to be in before your tank, you're useless, dead meat if you get focused.
Boots, RoA, Abyssal
So as stated in the ig-strategies for playing against Swain, Speed can be used as an effective weapon against him. Also he really benefits from MpR. Therefore the first item you finish should be the Sorc. Boots. They get you some more speed AND the MpR.
The first big item you want to get is the Rod Of Ages. Now the usual way to build Swain as I've seen it in most other builds and in most games where s1 played him, would be to go for Archangels first and then Rylais.
And as I think that both items are a really good choice, as they synergize just perfect with him (Archangels in general is a good item on casters and it also prolongs the time you can keep your little Tzeentch ravaging in the team and Rylai's is good for hard-stats plus the slow works good on your Nevermore and Lazerbird), I still choose the RoA over them.
1. Hard-statwise the RoA beats Rylai's due to its gold-efficiency. You get mana, AP and life (Durability!) in one item. Also, Swain arguably doesn't need the slow provided from Rylai's as much, because he has the hypnotizing Lazerbird.
2. Swain already has a good enough mana-regenartion without Archangels. Also, concerning Archangels, I'd say the time you can keep your ultimate activated (keep the damage going) with Archangels is not too far away from RoA's time-span (I might give that a try in a practice game some time).
Therefore I choose the RoA. It provides mana, survivability, damage and space (and therefore more time and gold for other items) in one go.
Next up is the Abyssal Scepter. I just love this item. It is, like the RoA, very well rounded and comparably cheap. It provides AP, MR (again, Durability!) and an MR-lowering aura useful to not only yourself but the whole team.
Another item I don't see on most Swains is the Hextech Revolver, ultimately going to become a WotA in this build. It has fairly decent AP and a good amount of Spell-Vamp on it (which I think gets majorly underestimated by most players and via Swain's Dot-Spells is great on him even when his Ultimate has a similiar effect). And if you can get another Aura-item to support your team even more in the process of boosting your dmg:
Hell, get it!
Next items can be pretty situational and usually I dont get much farther than getting the WotA, but even though...
Zhonya's Ring is one of the best AP-Items ingame and the active makes it even greater (especially since the CD is only 90seconds!). That's why I'd consider it a good choice.
If you find yourself getting focused by Raw-dmg and cc too often, you also might consider getting a banshee's veil. It offers even more survivabilty, MR and a good passive.
Another item worth to get with Swain is Lichbane (if you do so, start out with sheen).
It has MR, Speed, AP and, considering your AP and a decent passive which's Burst opportunities go well together with Swain's DoT- Characteristics.