Galio is one of the most underplayed champions in the league, as a result most players don't know how to play or counter him. Following this guide, early game you will be untouchable and your Resolute Smite will do massive amounts of damage; and later on you will become even more resilient and serve as your team's tank.

Runic Skin; Galio's passive, it should be viewed more as "a nice bonus" than "something to build around"; really, if you want to play an AP caster, you should just go do that.

Resolute Smite; Galio's bread and butter, it can be a bit tricky to land, but once you get the hang of it you will be able to zone your enemies into oblivion. It does great damage at higher ranks so you want to max it first for early harassing power. Late game the damage will be far less relevant, but the slow is still extremely powerful for chasing or escaping.

Bulwark; you will want to use this every time someone takes damage, fight this urge. Early game overuse of this spell can run you out of mana incredibly fast for almost no benefit, so try to only use it when you KNOW someone is in for a beating.

Righteous Gust; I've heard arguments for leveling this as your primary nuke, I would only suggest this if you find yourself unable to land Resolute Smite on a particular opponent, so judge on a game by game basis. Personally, I don't bother with it until I absolutely must, this is mostly because I find that trying to land Q-E combos instead of just Q runs me out of mana far too quickly, and I find the speed boost underwhelming until later ranks.

Idol of Durand; this ability will make your opponents hate you, or you hate your team; its usefulness is completely dependent on whether or not your team can follow up on it. For instance, if your Katarina follows it up with her own ult, then enemies will die. On the other hand, if you flash in and drop it only to have your party sit there picking their collective noses, then you will get eaten and blamed for the impending defeat.

Start with Regrowth Pendant and a Mana Potion, health regen will make you a very hard target for harass early on, more mana means more Resolute Smite.

Your first priorities are a Philosopher's Stone, Heart of Gold, and Boots; providing you even more sustainability, some health to synergize with Bulwark and movespeed, with a healthy side of gold generation; you can buy these in whatever order, but I almost always go philosopher's stone > Boots > Heart of Gold.

Next up are Aegis of the Legion, Chalice of Harmony and Mercury's Treads or Ninja Tabi. Get Aegis of the Legion if you feel you're too squishy; Chalice of Harmony if you feel too constrained by mana; or upgrade your boots if you feel too slow.

Late game you will want to upgrade your Philosopher's stone to Shurelya's Battlesong and Heart of Gold to Randuin's Omen, leaving one open inventory slot. This build leaves somewhat lower MR, so a good place holder is a Negatron Cloak, which can then be built into a Force of Nature or Quicksilver Sash depending on if you need health regen, or CC removal more (I almost always opt for Force of Nature).

Early Game; You shouldn't be too aggressive with Resolute Smite early on or you'll run out of mana fast, once you have two or three points in it and have landed one on them, enemies will think twice before trying anything against you or your partner. Try to always position yourself between your partner and enemies as Regrowth Pendant will restore your health very quickly.

Farming; Once you have Chalice of Harmony you will have zero mana problems, so by all means drop Resolute Smite on minion waves for easy cash. Before Chalice of Harmony however, your mana is too valuable to waste on minions so don't use spells on minions unless you are full on mana and there are no enemy champs in sight.

Poke Fights; Resolute Smite is very effective in mid game poke wars, so use it liberally, make a habit of weaving in and out so that you can catch the enemy off guard more easily for Idol of Durand, also remember to self cast Bulwark when you move in to drop Resolute Smite as it will negate a large amount of counter-poke, as well as making resolute smite hit somewhat harder due to Runic Skin

Team Fights; When you see the opportunity, either run in (aided by Righteous Gust and/or Shurelya's Battlesong) or Flash in for Idol of Durand, try to remember to self-cast Bulwark beforehand, and use Randuin's Omen afterward.

Tower Pushing; Remember that you are very resilient (especially during Bulwark) so don't be afraid to tank a turret for your comrades if there are no minions around. This is especially important after winning a teamfight, as you will have enough time to take a turret, but only if you don't have to wait for minions to haul their lazy ***es up to it.