This is my first guide, so any comments/suggestions would be great. Galio is one of the most underplayed champions right next to Corki. I'm not sure why he's so underplayed, as I find him quite enjoyable to play. He has a haste to catch up to champions, a slow to slow them, and a huge AOE taunt ult that does a decent amount of damage. Of course, you have to be able to land his skillshots to really do damage.
Marks: Greater Mark of Insight - Magic Pen. I pretty much always take these. Seals: Greater Seal of Clarity - ManaRegen/5 per level. Flat mana regen may be better, because you get Chalice before per level even out to flat, but it's up to you. Glyphs: Greater Glyph of Force - AP per level. Could use flat CDR or scaling CDR if you have problems with skills being on cooldown. Quintessence: Greater Quintessence of Insight - Magic Pen. I generally prefer the extra Mpen, could take Fortitude for the health or flat AP.
I generally get E first for level one teamfights, as the haste can be very helpful in retreat/chase. After that, I max E/Q evenly. Shield I get when teamfights start happening, as I dont really need or use the shield in lane. You can always get it earlier if you need it earlier. Ult whenever possible.
Starting Items: [img=items/meki-pendant.png][img=items/health-potion2.png] Early mana regen so you can use skills more often. Core Items: [img=items/chalice-of-harmony.png][img=items/mejais-soulstealer.png][img=items/boots-of-speed.png] I get the Chalice and boots first, to harass that much more. I also find getting stacks and keeping stacks, whether through kills or assists, is fairly easy on Galio. This build assumes you will get stacks, and out of the many Full-AP Galio games I've played, only once have I had to sell my Mejais. Boots: [img=items/mercurys-treads.png] (vs CC, especially to get out of stack-threatening situations) [img=items/sorcerers-shoes.png] (get ALL the kills) [img=items/ionian-boots-of-lucidity.png] (CDR, for the skillspam) End Game: Boots + [img=items/mejais-soulstealer.png][img=items/rabadons-deathcap.png][img=items/guardian-angel.png][img=items/zhonyas-hourglass.png][img=items/rylais-crystal-scepter.png] After I get my chalice/boots/mejais, I generally rush my hat starting with NLR. Depending on my amount of stacks, I either get GA soon, or keep going for damage. Zhonya's provides additional armor for ult purposes, and Rylais provides an additional slow on your easy to hit E and Ult.
If you can play safe yet smart enough to pull it off, Galio has a ton of potential. ALT+W > Flash Ulting into their team can instantly win a teamfight, and net you 5+stacks. I do realize this may be a pubstomp/troll build, but it is quite fun and with Galio's recent buffs, he has even more survivability in a Full-AP role. The least you can do is give it a try.