Firstly these are the setups i use for swain.He's very good on both ap and ad.
NOTICE:
Ad build is a bit tricky.Nomather what , torment ability must be maxed since it provides you +20% more phsical damage.
This is no trolling build,i'll upload a few "proofs" to confirm there's no trolling.
Playing him properly on mid you can beat almost all enemy champs.
Hope this guide will help you guys
Cheers

This page is mainly focused on ad,since ap is easy to play and understand(added bottom ap detailed)
Begginning:
Firstly dorans blade helps you with the extra damage and lifesteal,max out E (torment) as soon as you can,also you need attack speed : berserker's greaves are the best choice.And continue with the item order sequence.On mid you need to continually harrass the oponent with your torment(it does enough damage even if you don't hit him),combining root with e and a few hits will greately injure the opponent.


Secondly you need critical hit(here you can test out some crit runes if you want) , beacouse this is the most important thing that swain needs.
Late game
You'll become a higly targeted champ,and to prevent that you'll need warmog to get a lot of health and atmas impaler which will expand your ad a lot(converts 2% of your health to attack damage),you'll arrive at around 350 ad.In the end if you want 100% crit hit sell berserkers and get another phantom.Also ad Swain is a great farmer,and a semi carry haha.
I've never seen a swain playing attack damage , so i thought wt*?!? , and i tested this out on dominion beacouse you get more gold,and in this way you can learn this attack damage concept.Many will say at the begginning "ololo rep noob swain..etc" ,but they'll say at the end gj swain. haha

This is my first build so don't flame it too much.
Here are some pics to support my crazy concept:****EDIT****
ADDED AP BUILD DETAILED BOTTOM.

I've been playing Swain on ability power since he was released,and i consider myself a veteran with this champion.
Firstly what you need is doran's ring,it will grant you enough health,mana regen ,and ap to confront all kinds of enemies.
Swain's most important skill is Torment,it burns your opponent for a large chunk of health points.
Try to last hit minions beacouse you'll get mana,and this is a great thing,since it will let you stay a lot longer on lane.I seen a lot of swain's which buy mana/hp part (rod of ages).It's pure nonsence,the more ap you have ,the more trouble your opponents have.You won't have mana problems with this build if you'll use properly the skills.
Sorcerer shoes are also the only choice you'll have,since other boots won't help you.(If you want to spam try out Ionian boots).
Hp is also very important,buying Rylay's Cristal Scepter will make you pretty resilient to all kinds of attacks(combined with the runes i've shown you).Then you can get only ap.(notice: you can improvise,my build is not "godly" ,if you need more hp take rod of ages).
Rabbadon's cap will help you a lot,and in combination with Zhonya's hourglass will deal lots of damage.Void staff will help you even more when you'll encounter tanks with magic regeneration.
At the end,as a last item you can try hextech gunblade,and doing so you'll create a hybrid Swain with lots of ap and a bit ad(which will be a great last hit).
Forgot to mention: torment + ignite will melt any squishy opponent on mid(as long as he's under lots of hits/half hp)

Flash and Ignite for both concepts.

AP Build:
Pros
-Lots of damage
-Fast hp recovery
-One of the most resilient mages.
Cons
-Really fun to play,but tricky to master.
-Hard at begginning,may have problems with mana

AD Buid
-Lots of fun,you'll lololo each time you crit your enemies for half hp,even Gangplank will have envy on you :))
-Immense damage(criticals)
-Will make your opponents " :o WTF!??!?!"

Cons
-Hard to play
-Need a lot of practice
-Low mana(you won't spam too much with Torment if you don't farm)

Swain's a great farmer,just point root on a crowd of minions and use ultimate.It will grant you lots of gold(both ad and ap).
You can go in jungle and do a few mobs if you need extra bucks since swain can be resilient against jungle mobs.

I'll start out with ad.
You'll need to stay behind your allies and under no circumstance jump into your enemies.You are not a tank.Stay behind hit enemies ,fall back,don't underestimate them.You'll die a lot of times until you'll learn this.
Your teammates are the most important for a swain nomather what he's using(ad or ap)


Now ad
Almost the same thing as ad ,only that you can jump into them since you give a huge damage in the nearby area.Ap will regen hp,your opponents will die, good game.

This is my first buid,and i'll appreciate any kind of commentries (bad or good).
Thanks and i hope this build will guide you to master swain.