Early game- Galio excells at early game harassment. start of with meki pendant and health potions. spam resolute smite on your opponents and bulwark your lane partner as needed. You should be able to zone suppress your opponents and get a couple kills while youre at it. dont teleport back untill you have enough for chalice. When you get level 6, youll be able to ult you or your partner a double kill. continue playing agressively but staying out of opponents range untill lane phase is over.
Mid game- Played correctly, Galio is one of the most usefull team fighters in the game. BE THERE FOR TEAM FIGHTS. the best way to initiate with Galio is to wait for your opponents to cluster together then flash in, BULWARK, and ult. Done correctly, this ensures a win for your team. make sure to bulwark yourself before the ult, if nothing else, its discouraging for the other team to see that all five of them targeting you actually heals your character. making yourself present in every team fight puts your team way ahead. and you should have enough gold from assists and occasional kill to get a late game item or two.
Late game- Ok at this point you have Guardian angel, Frozen heart, and at least a negatron cloak for your Banshees veil. take your opponents agro, resolute smite the kids who run , tank some turrets. Galio is pretty much unstoppable at this point in the game, often being able to escape 5v1s. when you get your sceptre your ult gets a good buff, and finally if the game permits, trade in your chalice for force of nature or a rabbadons. Now go make the sentinel proud!