Well, if new (or returning) to a champ, I suggest you look him up on solomid.net or similar, it's always helpful. You don't have to follow it to the letter, but it gives good general knowledge.

Now, as to specific advice. Swain's passive gives him mana sustain, if you manage it well. I advise going either 21/9/0 or 9/21/0 depending on playstyle and what your team needs; you don't need the 9 in Utility. Level Torment first, then Nevermove. Some people suggest maxing Nevermove last, but I like it second, especially against a pushing opponent; it will give you the power to push back. You can more easily land your snare if you slow them with Laser Bird first. Unless they are a mobile champ like Ahri, you'll either force a flash or land your snare.

Early game you want to harass when you can, but your main goal is to stay in lane and farm up until you can buy Catalyst. After you have it and hit six you are pretty much immovable, which is my favorite thing about Swain. By this point you want to trade very aggressively when you can safely do so, as your sustain will let you win every single trade. You'll be forcing many mids to go back much earlier than they'd like, while you get ahead on levels, farm, and items. After you get RoA and Revolver and defensive items (if needed), you're golden.

Furthermore, remember to autoattack; Swain wants to trade aggressively due to his sustain, and his Torment makes his attacks do twenty percent more damage at max level. Basically, as Swain early you want to play it safe since you don't have sustain yet, but you still want to be a total pest to them when you can. If you're in range hit them with Q+E and an autoattack or two, then back off. Farm up, get items, dominate.

And, you probably know this, but a crucial bit of playing Swain is to not ult for too long. Turn it on for a few birds to gain back some health, then turn it off before it drains too much mana. Then repeat.

Let me know if you have any questions, and sorry if this was somewhat rambling.