Swain can be divided into three stages (In my experience).
Go for the kills. Your E will allow your auto attacks to hit for a good moment.
Your Q allows an easy combo of all abilities - E-Q-W, then flash ignite and ult.
You can essentially harass your enemy out of CS for most of this phase - You should find it very hard to be successfuly ganked provided you don't play stupidly aggressive. If a jungler comes, throw up a slow at whoever gets closest, and W the other. If one of them has a dash, place the W over your character as they enter range or slightly behind - then throw up R to get health back as you run.
Level>7 until late game
You should begin finishing core items; RoA, Zhonya's, etc. Prioritize items to counter the enemy team.
When able, gank other lanes or support whatever carry is struggling. It's more important to ensure an ally doesn't fall behind than to compliment an already successful lane.
If going bot, always prepare to W the support - Killing him ensures the carry will likely retreat, and your team should be right with you to finish the job. If going into a solo lane, treat it like your earlier phase - Flash, Slow, E.
Late game -
You build tank, but have the power to follow through with a kill easily.
In team fights, W the support to make sure he can't cause chaos, then W/E the nearest vulnerable carry or support.
RoA / Abaddons / Liandry / Visage / Will of Ancients / Zhonya's / Ryali's
Boots and pure-AP items [Void, Abyssal] can be bought depending on flow of game, and composition.
RoA / Zhonyas / Liandry's are probably the most important.
Every bird will renew Liandry, Zhonya's provides you two seconds of free regeneration.
He's incredibly strong provided you can master W. It makes or breaks his laning through kills and escaping ganks, and will control the flow of team fights.