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 build is the most common build that I use for Galio.
Teleport: Great choice for any champion in my opinion. Especially good for Galio because he can port into a tower and push back a lane easily using his Q+E.
Flash: Also a great choice for Galio because he can flash into a group and use his ult.
9/21/0 is the best choice in my opinion.
0/21/9 can also work, but I personally like the 15% increased penetration that comes with 9/21/0
Early health is a good choice for Galio. It allows him to not worry about going back too soon. You should easily be able to get to level 6 before heading back in most cases. Magic resist and magic pen are also good choices, because the magic resist gives him AP because of his passive.
Start with E (righteous gust) and max it first. It is easily the most all around useful spell Galio has. Not only does it have a decent amount of damage, but it can be used to get teammates out of bad situations.
Get Q second, and max it second. Its a good comp with the E, and eventually you can kill entire minion waves with these 2 spells.
Get W third, and max it last. It's a great support spell, but isn't as useful as the other two skills early game, in my opinion.
His ultimate is deadly, especially against heavy DPS opponents. Although Galio will take damage with it, if other teammates are close by, it shouldn't be enough damage to matter. Also, his ultimate teams up great with teammates like Kat or Amumu, or any other champion with an AoE ult, for obvious reasons.
Start with a meki pendant and 2 health potions. Be careful early game not to spam spells too much, focus on getting last hits and some harassing. I wouldn't suggest going for any kills until level 5, when you have W (bulwark) and can have that and righteous gust for escaping.
Make a Chalice of Harmony with the meki pendant, and also get Mercury Treads. Chances are good that if you have stayed in lane last hitting until level 6 or 7, you will be able to afford both when you return to base.
Next, get Banshee's Veil. By this time, you're probably in mid game, and the shield every 30 seconds helps tremendously on the other team's attempts to gank you. Also, the magic resist gives you AP with your passive.
The next item to get is Abyssal Scepter. This is, by far, the BEST item in the game for Galio. Not only does it give straight AP, but it also gives AP due to the magic resist that it gives. It ends up giving Galio around 107 AP.
After getting Abyssal Scepter, get more. You can also get Lich Bane, but I personally prefer Abyssal Scepter, because it's cheaper than Lich Bane, and you're getting about the same amount, minus the movement speed and the Lich Bane passive.
Tanking with Galio:
I don't play Galio as a tank often. I don't feel like he's the best choice for a tank. He should be considered a high HP caster, who can tank if necessary. If your team forces you to be the only tank-like champion, consider getting aegis early, and getting a guardian angel after your first abyssal scepter. If the other team is high DPS, get thornmail. Although thornmail will make your ult slightly less powerful, it will cancel out with the amount of damage the character will be doing to himself by hitting you.
Thanks all for reading.