Swain the AP tank, When played right will absolutely destroy and frustrate enemy champs but be careful you don't do burst damage so no running headlong into the enemy team thinking you'll wipe them all out. Everything you do revolves around DoT's and punishing people who try and push.
Runes: Marks: Magic penetration, there is no alternative.
Seals: I go flat armor because it helps with Swain's weakest time, his early game, but if you feel comfortable feel free to go AP per level, or mana regen per level.
Glyphs: Once again I focus on defence and go flat MR runes. But since you most likely will be building a MR item feel free to go with AP per level or magic pen.
Quints: There are only two options for these, flat AP or magic pen. It can go either way depending on what you feel like doing, AP to start off stronger, or Magic pen to have increased heals from your ultimate and spell vamp.
Masteries: I go 9/0/21 Because I still believe that utility is good for Swain even with the new masteries.
Offense: Mental Force, Sorcery, and Arcane Knowledge.
Utility: Summoner's Insight, 1 in Good Hands, Expanded Mind, Swiftness, Meditation, Runic Affinity, Awareness, Intelligence, and Mastermind.
Summoner Spells: I go with Ignite and Flash. Ignite when combined with your E will do serious damage. Flash is an all around great tool. Helps with ganks, positioning, fleeing, etc. The only other spells I would consider is teleport so you can return to lane faster or join a team fight quickly, and Cleanse since it is nice to be able to remove CC from yourself.
Passive: Carrion Renewal
Whenever Swain kills an enemy unit, he recovers 10 mana (+1 each level).
Great passive for Swain. Allows you to sustain in lane for longer if you don't have blue buff.
Swain sets his raven to cripple an enemy. Over the next three seconds, the target takes 25/40/55/70/85 (+30% ap) damage (per second) over time and is slowed.
Cost 60 / 70 / 80 / 90 / 100mana
This skill is a tether that deals decent damage but more importantly slows enemies. That slow will allow you to set up your W and can pop Banshee's Veil which is always a good thing. Since it is a tether skill don't cast it at its max range because they will run from it and make it useless.
Swain marks a target area. After a short delay, mighty talons grab hold of enemy units dealing 80/120/160/200/240 (+70% ap) damage and rooting them.
Cooldown 18 / 16 / 14 / 12 / 10seconds
Cost 80 / 90 / 100 / 110 / 120mana
Swain's AOE Root. This ability will make or break you. Hitting it right will win fights so get practicing. In lane this can be used to zone out or punish champs that are trying to get creep score. In a team fight try to root multiple people but if you can't do that then just get the squishy.
Swain afflicts his target, dealing 75/115/155/195/235 (+80% ap) damage to them over time and causing them to take 8/11/14/17/20% increased damage from Swain's attacks for 4 seconds.
Cost 65 / 70 / 75 / 80 / 85mana
Swain's main harass ability. Good strategy is to use this then do an auto attack or two since they take increased damage for a short time.
R: Ravenous Flock
Toggle: Swain transforms into the form of a raven, during this time up to 3 lesser ravens strike out at nearby enemies dealing 50/75/90 (+20% ap) damage each second. Swain is healed for 75% of damage dealt versus champions, and 25% versus minions. Prioritizes champions
Cooldown 15 seconds
Cost 25 mana
Time to impress the ladies with your Ravenous Flock. This is what makes you the tank that you are. Always have this ready for team fights, if it's on cooldown wait and then go in when it's up. The raven's prioritize champions and will activate the slow on rylai's which if down right will have 3 CHAMPS SLOWED so no escape once you hit the scene.
Starting items: Boots and 3 Pots. More mobility and sustain nothing else needed.
Core items: Rod of Ages, Rabadon Deathcap, Sorc Shoes, and Rylai's Crystal Sceptre. RoA gives more mana, health, and ap, RD gives massive amounts of ap, and sorc shoes give more movement and increased damage.
Your final two items are dependent on how the games going.
Against heavy AP: Abyssal Sceptre and Banshee's Veil for increased MR plain and simple. Against heavy AD: Frozen Heart and Zhonya's hourglass. Both give armor and Zhonya's gives ap and Frozen Heart gives Cooldown Reduction reduces attack speed. Against Tanks: Void Staff and Deathfire Grasp, Void gives more Magic penetration and Deathfire gives more ap and mana regen as well as having an activate ability that deals damage.
Early Game: This is the hardest time for Swain. Try to harass with E and get as much CS as possible. Your first trip back to base you should get a catalyst to build into RoA, but if you don't have enough gold get a dorans ring and part of the catalyst. And of course get wards to cover your ass.
Mid Game: Hopefully you have been given blue buff and are now a terror to all around you. You can now farm creep waves very effectively with W and R. So it's time to roam around a bit and gank in the other lanes.
Late Game (AKA Team Fights): Wait for the initiate and then when you see the opportunity use your W to cage someone and then use E and Ignite on them to destroy them with your teams help. You should always have R up in team fights as it heals you so you can run in to hit your E and Ignite and will allow you to passively harass other champs that are trying to get you.