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.
Galio is not a tank due to his passive ability but in order to make his passive affective you need magic resist. This makes him a hybrid. He is slow-moving no matter if he has mercury treads or not... so get his boots a little later than regular characters. Ghost will give him necessary movement speed when the time is right, and ignite will provide damage when Galio's skill are on cool down or if he is out of mana. (He is very mana dependent early game because Righteous Gust and Resolute Smite are expensive. That is why Meki Pendant and Chalice of Harmony are necessary early game.
His masteries depend on what level you are, so if you are a low level get resistance and haste.
Galio's skill combination start with resolute smite to slow his opponent, and Righteous Wind to speed Galio up and deal extra damage. Then, as you catch up, ignite them and ult. That will draw them toward you, taking damage from ignite, and your ult can finish them off. Thats a perfect situation against someone weak or any spell caster.
In a troubled situation, pop bulwark and ghost. Then send your Righteous wind in the direction your running to speed you up even more.
Being fed early game around level 7 or 8 can change the course of the game. If galio is 1 vs. 2 in a lane if you have a jungler, or if, during a team fight, the rest of the enemy's champions are away and a lane is open to feed on, take it. Galio can resolute smite groups of ranged minions and he can righteous wind the incoming minions in a line. Then, if Galio is ganked while feeding, pop your ult and send the ganker on the defensive, slowing them with righteous smite and dealing damage with ignite right after your ult and righteous wind them to increase your speed and deal more damage.