Pros

-Can farm and lane for a long time
-AOE root
-Can heal back from harass
-Deceptively strong dot damage

Cons

-Countered by Ignite and other heal reduction effects
-Stunned before in ultimate form usually spells death
-Carry status drops off in late game

I use generic caster runes:

Flat Health Quintessences
Magic Pen Marks
Mana Regen per level Seals
Ability Power per level Glyphs

9 / 0 / 21

Important Talents include:
Archaic Knowledge
Awareness
Meditation
Utility Mastery
Intelligence
Presence of the Master

Start off with a Doran's Ring.

On first trip back, be sure to grab Boots of Speed and hopefully Catalyst the Protector.

On the second trip back get Rod of Ages and upgrade your boots.

Flesh out your build with Rabadon's Deathcap then start buying some survivability items (Banshee's Veil, Abyssal Scepter, Zhonya's Hourglass and Guardian Angel are great, build against what the other team is doing best with).

Don't be scared to sell your Doran's Ring to buy that high tier item or to stock up on wards.

Level 1 - 5

Play safe until you hit level 3, but always be on the lookout for harass opportunities.

Last-hitting is doubly important for Swain, as it is a source of income as well a mana regen mechanic.

Against squishier folk or brave opponents, you can easily land a kill with the following combo:
1. Lead your opponent with Nevermove
2. Walk up past your maximum attack range
3. Nuke with Torment + Decrepify + Ignite
4. Chase with autoattacks

Flash forwards or backwards when necessary to land the kill or avoid your own destruction.

Level 6 - 12

This is (usually) your strongest point in the game.
The enemy carries are on their way towards high end recipes but still don't have the damage for a sustained bout against your ultimate. Tanks have some items put together but can still be nuked. Other casters can burst hard but can't sustain themselves.

In order to put yourself and your team in a great position for late game, start warding the river and ganking sidelanes.

You can also jungle if you want to give extra experience to your lanemate. You can grab Ancient Golem at level 6 onwards (and you should) so as to be a constant presence in the lanes.

Work with your teammates to gank enemies.
Nevermove should be your initiate followed up by Torment, Decrepify and Ignite.

In teamfights, you can save Nevermove for hairy situations in order to trap their carries or save your own. Your Ultimate should always be ready for teamfights, but be sure you have the mana to sustain it. Also, know when to turn it off. It's a lifesaver but also a mana-drainer.

Level 13 - 18

Diligently ward important areas and crossroads and be sure to stay together with your team when not farming safe zones.

Your damage starts to fall off but AD carries become monsters in late game so get some life insurance items (Banshee's Veil vs stuns, Guardian Angel, etc). Along with that, tanks can fully absorb your combos so be sure to land them on more important targets.

Work with your team to disable important enemies and land big nukes on their carries. If you are going to die and can't escape, be sure to do as much damage as you can to their carries so that they won't be able to push effectively if they win the teamfight.