I'm just gonna go over the basics nothing fancy. Swain has some good damage over time but I feel building straight AP is better saved for your nuke/carries. His tank potential is way too good to ignore so I build him off tank.

Flat MR, Armor and Health are crazy good to keep Swain in lane until level 6. I don't think I've ever recalled at mid before level 6 since I started playing these runes and usually if I'm last hitting well thanks to Swains passive I can stay in lane indefinitely thanks to his ultimate. Magic Pen is a must as it will make harassing and potentially killing the enemy mid a lot easier.

These should seem fairly obvious based on the runes. Stacking the extra health, armor, and MR gives you a ton of survivability early game, and late game Ardor gives you a pretty good AP boost. Also the extra magic pen in offense is very important.

Ignite is extremely effective on Swain as it stacks with his Torment to do even more damage. Flash is just an all around amazing summoner spell.

I used to have something big here, but I changed the items so I don't feel like rewriting.

E is the big damager as it buffs the damage of every subsequent attack. Generally I look for opportunities to snare the opponent with W. If it lands I can quickly run up and E then Q. They should exit the snare as you land your Q and if they are running the slow should allow you to catch up to tag them with Ignite. If they try to counter harass with a skill shot I like to flash out of the way giving me a huge lead on the enemy mid. Some counter harasses will be unavoidable but because this build is tanky it's almost always ends in your favor. At level 3 this combo does more than half life on most character's early builds, but if you are fighting someone with a ton of life steal (e.g. Vlad or Vampiric Scepter Vayne) it's not particularly worth it and you should save mana for when you hit level 6.