Just try to jungle a bit in the beginning and maybe if there's any ganking potential try to go for it but if there aren't any real opportunities just keep clearing your jungle until it's lategame, cause that's where galio is best. :) Try to look for some good teamfights and maybe even flash-ult in there, if you can hit 3-4 people your team should easily be able to drop all kinds of stuff on them and kill them.

Have fun! :)