Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This guide will show you how to play Galio to it's extreme. You will be able to start teamfights without dying, farm creeps, defend the base very well, and push like only a few other champs are able to. But most important: you can deal a looooot of magic damage.
Why heal and ghost?
You will want to have heal. It's just great, since we won't have that much life, it can save your life, or make the enemy champs do some stupid actions, to get you near the tower and you will just heal, turn back and kill them, before you are killed.
Ghost is important to chase champs. since galio has a good source of slow already, you can run after the enemy, slow them (and do good dmg) and then you team can get him. Easy.
You can also use it to run away faster and save your life ;)
First you will need to get chalice of Harmony. Galio needs too much mana to spam his abilities all the time. But using the chalice, you will be able to keep using your Rightous Gust against the creeps. You even will need it in endgame. the buy mercury boots. They are awesome. +magic resist (that means dmg) and a good anti-slow effect. Next is Banshee's Veil. You want it because you will start the fight and get some stuns, so get it and keep it. Abyssal Scepter is next since it adds about +100 ap.
Thornmail is the easiest (cheapest) way to get a lot of armor, and hey, it really fits good to our ultimate. You get less damage, and the enemies will nearly kill themselves? Awesome! Throw then 1 Gust and 1 Smite and they should all be dead.
After that get Zhonya's ring. more ap and a little life saver. If you are in trouble, activate it and hope you teammates kill the rest of the enemies, so you can first take the focus and then go back.
and finally Lich bane! I only got it once with galio, and I just backdoored the enemies base. 1 hit will do 500-600 damage, but you probably won't get it. The other team rather gives up or you just win before you can get lich bane. But if you do, you'll rock like a living stone! Of did I say it adds 95 Ap instead of 80? ;)
A few Hints:
try to not play that offensive early game. Stand behind the creeps, and if you think you can kill 1-2 creeps, use your gust, so you don't need to go to close to the enemies. It often isn't wasted, since you can hit the enemy champions, too.
if you are in endgame and run away with a couple of hitpoints, but your mana is still nearly full, go jungling and use your bulwark to be healed. You only need to use it twice and your life should be full again. So you won't need to go back completely.
Always use Bulwark before using your ultimate. This helps you to survive (especially when the enemy play dps champs)
Never run into towers. They are deadly. You don't have as much armor and life as other tanks, so never play to offensive.
use your smite to slow enemies, who run away. you can even use Ghost for this purpose, so do so!