For Runes the rules are simple: You get as much Magic Penetration as you can, some mana regen to help you with your AWFUL mana pool, Cooldown glyphs to reach 5% (15% along with the masteries, 35% along with frozen heart) and you have a glyph to spare... I use it for Magic resistance just to get that 1 ap more but it's really up to you if you find it ridiculous to play with a rune unlike all others, and want to play them as a set.
For Masteries make sure to take ap on attack tree, cooldown reduction, and magic penetration and max out the utility tree, taking cooldown reduction wherever possible and mana masteries. I also master the utility spells as I use Flash and Teleport, getting a profit in both.
Galio AT rule no.1:
Your mana is FREAKING ending soon!!!!!!!
You want to spam your abilities, to farm as much as possible, but your mana is really low. So? So your first buy is mana regen item. The Chalice of Harmony is perfect. It is cheap, and can save your mana throughout the game without a problem. I start with the MR part of the item, for those 12 AP and the defense against my potentially AP enemy in mid, but it's in your choice.
Then the boots. 35 tenacity, 25 MR, 12 AP. Why not? Because some go with sorcerer's. That's a choice too, but I prefer Mercury's Treads for movement.
Now you have good MR, decent AP, movement speed, hopefully a kill or two but you are still fragile. Next step: Zhonya's Hourglass. Tons of AP, and maybe the best active item in game. Not bad...
From now on the order is not that standard, you can get the items in any order you wish, depending on the game and your opponents.
My preferences are:
Rabadon's Deathcap: What the hell of a caster are you without your hat? tons of AP plus even more from passive, pluss even more from passive combined with your passive. Pure Ability for a pure nuker.
Abyssal Scepter: Ability Power, Magic Resistance, and guess what? MORE Ability Power. This item practically cries out: "I was made for Galio, baby!!!"
Athene's Unholy Grail: Upgrade your chalice, to get more AP, some CDR, and a couple cool passives... Not bad, huh?
Soooo final item. Usually while building champions I use my last slot to cover any weaknesses the champ might have. Until now Galio has two main weaknesses in his multi-role in this game. Low health - low armor. You will find items like Thornmail really useful, but still on 1800 max hp youre not tanky, you're just a laugh. A warmongs would leave you with low armor. So my choice would be either Sunfire Cape or Rylai's Crystal Scepter, which might not give you armor, but enough health, many AP, and a cool passive as well (a tad useless on galio though, his spells are aoe and one of them is slowing already, but still...)
Now seriously lets face it. You have enough AP to deal about 2000 dmg in 2 seconds, you cant die easily (high defenses, zhonya's active), have decent penetration (don't forget to add abyssal's passive too) and you can be a great support (all 4 spells can be used to aid your allies). You can defend, attack, support, pretty much everything.
Farm as much as possible. After level 6 cast at the same time your Resolute Smite and your Righteous Gust at the caster minions . It should be enough to give you 3 free minion kills
To summarize it's a balanced build to play as an AP offtank, emphasizing in AP.
-Many passives grant you too many advantages
-Great farming (surprisingly good for Galio)
-Element of surprise (no one will expect you to deal that damage)
-High damage but not "DAT BURST" you get with other champs/builds
-Not really a tank
-If you played Galio as a heavy tank before, you should see a big difference in his survivability. The thing is that when you get chased by a high damage opponent, you dont run away. You just kill them. Remember, you CAN do damage. And if you do remember, your opponents will. For ever.
And before this guide ends, I have to repeat what you will hear in EVERY galio AP build, that yes you can stop your ulti earlier by pressing R again and still do full base damage. That is, when you want to ensure your kill (YOU grabbed em, didn't you? ;) ) before your teammates steal it. Believe me, you need to learn to do it.
That's is guys, I hope I made my points, the build is at your disposal. Good luck and have fun using it and I'm eager to hear ANY feedback you may have. GGaliOP.