Not Updated For Current Season
Start off with a Dorans ring and a health pot. This will give you some nice mana regain as well as health.
I went for a normal caster build. Once you get the zhonya's ring sell the Dorans ring and buy yourself an rylai's crystal scepter for a bonus slow as well as some hp.
The first thing you should know about Swain is that he is very squishy as well as mana hungry early game.
Make sure to stay in a group and harass as much as you can.
You will only be in big mana difficulties before you get your tear of the goddess.
Open up with Torment then use Decrepify. You then need to aim your nevermove right ahead of the other champ as they are in the slow. If they are still not dead pop Ravenous Flock. Remember you can still cast spells in this form. BUT! be careful your mana drains as your Ravenous Flock is up. Once done with this rotation and the other champ is dead. Last hit minions so you can get your mana back up.
Hope you have fun!