I am just starting to learn this champion and his potential to turn the tides of war, so bear with me as I describe this build. It is not meant to be a top tier build, but rather something easy to get used to building as you practice with Swain.

Basically, it is a simple build for newer players to learn, as well as a placeholder for my own Swain build.

I picked this sequence because you will have to rely on the damage of your Q and E skills to really put the scare into your opponents. As a mid player, your W skill will be most useful as a harassment/zoning skill because it has the furthest range, but if you lane, it will be used to cut off any enemies who decide to run away.

Whether you go mid or lane with another player, once you get your R, pushing and holding becomes easier. Because of it's short cooldown, lifesteal and toggle option, it is a great way to farm lots of minion kills. Feel free to jungle a bit if the lanes are pushed a bit. In the early game, Swain tends to miss out on a lot of gold, so it's important to find minions to farm once you get your R.

In team fights, I tend to go down the line of attacks. Open with Q to put damage down and slow your target, followed by W to root them. Hit R, then E to deal constant damage. By then, Q should be ready to fire in a few seconds and you can chain another combo together.

Be careful with your Flash. Swain has pretty bad mobility by default, and boots barely bring him up to par. If you Flash, understand that you have no means of escape after it, so use it with caution. Swain doesn't nuke enemies, he kills them over time, so Flashing into a fight for a gank is usually not a smart choice.

Ignite is a solid spell because it allows you to add onto the DoT's you already have. Your E is essentially the same as Ignite, however you should save Ignite for after your E has dissipated. Ignite helps turn burn off a lot of health that tanks stack, however it is not something to spam. I find it is best to take out the glassy/squishier enemies with Ignite and skills, as they will usually go down in a matter of seconds. As a note, this build does not have the Mastery that allows for increased AP when Ignite is on cooldown, so do not rely on that slight increase after Ignite has been used (it won't make a terrible difference anyways).

The two item you want to get right after your starter items are the Sheen and Hextech Revolver. Which one you build first is up to you, however I tend to build low and slow. I start with cheap, easy to acquire items and then snowball up. Swain misses out on a lot of gold in the early game, so getting cheap but effective items is key to succeeding. The Sheen is great for adding an extra punch to your basic attacks, especially after you land your W and root your target. The Revolver helps you after level 6, when you get your R skill. The AP/Spell Vamp combo works well with the ult, since you'll be receiving a lot of health back.

The Chalice of Harmony and Fiendish Codex build into Athene's Unholy Grail, which is an important item for Swain. On each kill and assist, Swain gets 12% of his mana replenished. In team fights, this means Swain can toggle his R and leave it on for a long time, given that kills and assists are being achieved. Plus, the AP and Mana Regen are big bonuses for Swain players.

The Revolver will build into the Will of the Ancients, then get the Giant's Belt to give Swain a bit more suvivability. This will go into Rylai's Crystal Scepter, which will make Swain a tanky heavy hitter.

If, by some miracle, you still have money and time left in the match, go ahead and build the Sheen into the Lich Bane. This typically won't happen, however in some cases matches last longer the 50 minutes, and will allow you to build up to it.

Once you get your R, feel free to farm large hordes of minions with it. It's cooldown is about 10 seconds, so don't be too conservative with it. However, keep your eyes open; no one wants to be caught far from their turret with their R on, barely any mana and no teammates around.

Also, after you have pushed the enemy to the second row of turrets, it might help to farm the jungle minions, given that your team does not have a dedicated jungler.