Hi, welcome to my guide on how to play swain! First I would like to say I am not a professional so this guide may not be perfect.. BUT! This guide has worked for me and has given be a very high w/l ratio with swain. Any guide I put out has been tested, and has worked. I will never put a guide out that I feel will not help someone else.

PROS:
-Excellent 1v1er.. possibly the best 1v1 in the game.
-Great bully in mid or lane, always keeps enemy low.
-Excellent at getting clean ups because of all his DoTs(Damage over time)
-His dots+ult does IMMENSE damage.
-Very tanky and extremely useful in team fights due to his ult.

CONS:
-Very weak until you get to level 6
-Once your mana runs out you're in a lot of trouble in terms of survival.
-Very item dependent.

Ignite
I use ignite because ignite + swains other dots is amazing and great for getting those early game kills.

Flash
I get flash for better survival.

Greater Mark of Magic Penetration
I get x9 of these marks because it will cut through any magic resistance which will ultimately lead to you dealing more damage.

Greater Seal of Scaling Mana Regeneration
I get x9 of these because Swains mana runs out very quick, this added on mana regen will help with Swains mana a bit.

Greater Glyph of Magic Resist
I get x9 of these for better survival vs AP champions.

Greater Quintessence of Magic Penetration
The more magic pen the better!!

Greater Quintessence of Health
I get this as my last quint for a little additional survival.

catalyst the protector
I open with catalyst for the mana and the passive help as well, plus it will be used in one of your upcoming items, rod of ages.

Sorcerer's Shoes
This is my next item, good magic pen!!

Hextech Revolver
Decent Ap, the spellvamp is helpful, and is going to be used in your up coming item

Will of the Ancients
Good ap, spell vamp is helpful, good aura for your team.

Rod of Ages
Excellent for health/mana and pretty decent AP as well.

Rabadon's Deathcap
What else can I say?? Excellent AP

Rylai's Crystal Scepter
You don't have to get this, but I like getting it. Has a great passive, good for health, and good AP

Your last item is going to be situational, look at what you need to counter your enemy's and get that item.

As I stated in my introduction, Swain is great in team fights. Whenever you're about to engage in a team fight use your ult before you engage, put your dots on the enemy that's going to be doing the most damage. Use your snare for fleeing enemy's. Rinse and repeat every team fight.

Swain doesn't really have any good farm ability's besides his ult. For farming just keep getting the last hit on the minions, that's the only thing I can recommend. I'll sometimes pop Swains Q spell to help farm a bit.

EARLY GAME:
In the early game I play fairly passive until I get to level 6. Then I play extremely aggressive trying to always keep my opponent low/ going B, which will prevent him from farming which means you'll get a gold/level lead over your lane. I feel like Swain is one of the best at doing this. Only go for kills if you know you will 100% get the kill. Play aggressive, not stupid.

MID GAME:
By now your build should be coming along and you can start looking around for some ganks/tower kills. Remember to always have map awareness when ganking. Don't try and go for a gank is minions are at your tower/if your tower is very low. The mini map is going to be your best friend in LoL, ALWAYS look at it. In a normal game I look at the mini map about 70% of the time. Doing this can prevent you from losing a tower, helping lanes in dire need, and prevent you from getting ganked.

LATE GAME:
By now you should have your full build and ready to rock and DoT. Swain does IMMENSE damage late game. You should be trying to group up with your team to push and get tower kill/inhib kills. Once again as stated above, check your mini map, watch for the enemy.

Swain is without any doubt in my mind one the most underrated character in the game. Most people think he's decent and leave it at that. I think Swain is a huge game changer when played correctly. He's great at pushing lanes, does amazing damage in team fights, can gank very well, has decent survival, and can absolutely dominate in late game. He's the whole package! He takes some time to learn, but man, when you learn him he's a beast!!

To end this guide I would first like to say thank you for reading!! Second, I would really appreciate any feedback/criticism. I'm just like you guys, trying to get better!
Please comment and vote this guide! I put some time into this guide and would really appreciate seeing your appreciation! I hope to write more guides soon.
I hope this guide has helped you guys learn something, if not, have a great morning/evening!
Farewell friends!