NOTE THIS BUILD IS FOR READING IT MORE CLEARLY ALL CREDIT GOES TO THE PERSON WHO MADE THE ACTUAL BUILD AND VIDEOS
http://leaguecraft.com/strategies/guide/8039-the-true-way-to-play-ggaliop.xhtml
i just copied and paste the Items,Skill sequence and changed the words a little (such as swears) so it will be easier and more appropiate to read and understand :)



This build does NOT FOCUS on the TANK ASPECT, forget that.. THIS GUIDE.. focuses on the HOLY-****-WTF-IS-THAT-AND-INSANE-DMG?!?!?! aspect. This is a FULL AP BUILD, and trust me.. GGaliOP REALLY has an I-WIN-BUTTON.
Play Video

WE NEED MAGIC PEN to hit hard, MANA REGEN for mana issues and skill spam, AND CDR for our ULT.
Greater Quintessence of Insight + Greater Mark of Insight = 14 Magic Pen
Greater Seal of Clarity = 16 Mana Regen at LVL 18
Greater Glyph of Celerity = 8,10% CD Reduction at LVL 18

10/0/20, non negotiable, we are NOT PLAYING as tanks, we are playing as PWNING MACHINES, we NEED the CDR (capping with golem) and the AP BURST FROM IGNITE in early games.

Core items:
1.+ 2=
2./(if they are all squishy, or they have no CC, PICK SORCERERS!)

3.
4.

CORE

1.

2.

FINISHING ITEMS
Rylai's Crystal Scepter - GOOD HP, remember.. we are playing as MAGES.. so we are too squishy, so 500+ HP is very nice, it also gives us +80 AP and makes our E speed-us +slows enemies.. so it's great.

Lich Bane - THIS IS A WIN LATE GAME.. AND A MUST, with this, we can push a tower/inhibitor/nexus with like 3 hit, remember.. the MR gives us MORE AP so.. +95 AP (+15 for our passive) + 30 MR + 300 MANA + 100% AP DMG ON MELEE HITS WHEN WE USE AN ABILITY.. it's SO GREAT!

NOW SELL YOUR CHALICE

Abyssal Scepter - Need more MPen?, ok.. +AP +MPEN +MR = GREAT ITEM FOR Galio, remember our passive.. this makes it to give us +100 AP +57 MR +20 MPEN.

Void Staff (ONLY WHEN THE OTHER TEAM HAS TWO OR MORE +100 Magic Resistance CHAMPS)

Deathfire grasp The other team has a fed Garen or a tank who rapes our team? OK, take this boy and kill him!

END GAME CORE

Runic Skin
Nice Passive, but most of the Galios fail when rushing MR items, thinking "OMG OMG OMG I HAVE a percentage OF MY MR IN AP.. OH NO LET'S RUSH MR!!!!!!!!".. NOT, this is an entire FAIL, so.. it is a nice passive, but not THAT important..
With all MR items (Chalice + Mercury + Force of Nature + Banshee Veil + Guardian Angel + Abyssal Scepter) you can reach 283 MR, that cost 12665 Gold, and gives you only 141 AP from MR, when Mejai cost only 1235 Gold, and gives you 180 AP, yeah.. you need to be careful and dont die, ok.. you can buy Zhonya for 3460 and it gives you 120 AP + 30 AP (from 25% zhonya passive) = 150 AP ONLY with Zhonya.
So.. it's a NICE PASSIVE, but not THAT nice to set your entire build on this.


Resolute Smite
This is one of our CC moves, with this we can slow and dmg an entire group of enemies, and combining it with our Righteous Gust, we can hit SO HARD that our enemmies go for /all screaming.. "CMOOON WTF IS THAT DMG?!".


Bulwark
This sheild is your key support, for healing and giving more armor to your teammates :D, MR? ARMOR? yeah.. thx for that (90 MR = 45 AP), it is useful.. but that heal.. O M G.. HELPS A LOT on teamfights, and combined with our ULT.. is a GG teamfight.
REMEMBER, you can put the Bulwark on your allys AND RECEIVE THAT HEAL ON YOU, this is an amazing move for heal you when you are back with low hp.


Righteous Gust
OK, that's it.. THIS IS ONE OF THE BEST SKILLS EVER (in my opinion), it gives us.. an INSANE DMG.. an INSANE move speed, and has an INSANE range. With a nice AP we can clean up an ENTIRE group of minions ONLY WITH THAT SKILL.. it is SO AWESOME!
Try to be smart with this, because this skill can buff the speed of the minions too, so.. if your enemy is close to your minions.. you can Q + E the enemy minions (try to put Q on your enemy), and YOUR minions go with a lot of speed to hit your enemy doing nice dmg because no enemy minions left alive.


Idol of Durand
The OWNAGE skill, that's it, nothing less.. nothing more.. Having a hard teamfight? Having trouble making an Ace? The match is lasting for too long? Ok.. Put your Resolute Smite in the middle of the fight, make a path to your enemies with your Righteous Gust, turn on your Bulwark, and bring your Ulti!
NOTE : DONT EVER FORGET.. THAT YOU CAN INTERRUPT YOUR ULT JUST MOVING, AND STILL DO DMG WITH THAT.

SKILL SEQUENCE
+ FOR FARMING MINIONS and harassing!!!!!! :D

1 - HARASS with Q + E everytime you can. You need to show the other team your BOSS POWER.
2 - You can SAVE a teammate putting your W on him when he is running away from another champ and taking down the enemie (or scaring him) with Q (slow) + E (more movespeed to your ally).
3 - TEAMFIGHTS, you need to warm up that *****ies with your Q + E, and when they have 70%/80% or less hp, we can RUN with E, SLOW them with Q, put your SHIELD with W, and ULT with your R.
BUT REMEMBER!!! when their hp is going down TOO FAST.. you can MOVE to interrupt your ulti, and KILL'EM ALL

Note : If you are ulting on a ENEMY TOWER, you receive the tower hits, and your ult HITS MORE HARD.

+
Teleport - WE NEED IT, this guide is more based on a MID/DUO LANE Galio and TELEPORT is a MUST on mid players, gives us SO MUCH MORE GOLD, with map control we can save A LOT of towers, kill entire groups of minions (making us rich) and participate in EVERY teamfight (dont worry if you are late, we can still make an ace, with our ult and help our friends to hit that bastards). We can PUSH when we have our LichBane (3 hit = tower down, this makes him a nice BD champion).
Play Video Ignite - HELPS A LOT in early ganks when the enemy runs away with no HP but our IGNITE :).. AND gives us a +10 AP when it is on CD (from Masteries)

Other Options :
Flash - we can SLOW them with Q and gain move speed with E to sit in the middle of the fight, BUT is still a GOOD Option.
Ghost - Ghost is useful to chase and escape and the syngery with our Gust is just amazing..

WE DONT NEED Clarity, we can SPAM our skills from lvl 1 to 6 ONLY for ENEMY dmg purpose. You need to position yourself in the RIGHT WAY to dmg minions AND champions, and when the Chalice is finished, we wont need to worry about mana issues.

When you reach lvl 5-6, you can Q + E the mid spot of the jungle while you are lanning, it's awesome how you can clear that spot while your minions rape the lane, more gold, more xp, for 2 buttons and 2 clicks and no walk.

You NEED to clean YOUR Lich spot and THEIR Lich Spot being this u can LVL UP more quickly than your enemy and ****ed up one spot of their Jungle, this can RAGE their jungler Champ.
Play Video GOLEM = This is TOTALLY NEEDED, Galio Ult has a HUGE CD of the game. We NEED the Golem, and with the mana regen buff we can SPAM our Q + E and PUSH a lot. With our Masteries + Runes, we have CAP CDR when you have the Golem (40%).
We can clean all camps with Q + E, so.. DO IT!, more xp.. more gold, go go go!

WE NEED TO FARM AS MUCH AS WE CAN, with this rule we ccould REACH LVL 18 with a 3/4 lvl difference on the other team, and this HELPS A LOT ON TEAMFIGHTS WITH YOUR ULT. When we reach lvl 16 and the other team is STILL on lvl 12/13.
Like this

So.. FARM FARM FARM, and when you are doing nothing.. FARM TOO, farm all the jungle (leave lizard alive for allies, and never do dragon alone, it takes too long)

PROS :

1 - Able to initiate any teamfight with our Q + E and take down 50% of hp from the other team.
2 - can farm minions with E, but.. in jungle we need Q + E
3 - We can enter in jungle with no hp, and come back FULL HP
4 - able to WIN a teamfight with our W + R

CONS :

1 - The ONLY ONE cons, that can make this champ almost useless, is CC Counters like,
Cleanse,
Quicksilver Sash,
Blitzcrank Power Fist,
Garen Decisive Strike,
Udyr's Bear Stance,
Xin Zhao's Three Talon Strike
Gold CardTwisted Fate's Gold Card
Galio after patch image:

Thanks for reading! :D
xFrozt

20/10/2010 :


Galio
* Righteous Gust mana cost increased to 80/85/90/95/100 from 70/75/80/85/90
* Resolute Smite mana cost increased to 70/75/80/85/90 from 60/65/70/75/80
* Idol of Durand mana cost increased to 100/150/200 from 100/145/190
* Idol of Durand duration reduced to 2 from 2.5

Mana issues is not bad, the spells now cost only 10 more mana.
Ultimate duration reduced to 2 from 2.5, told u.. nerf coming and the nerf is here, but Galio is STILL awesome, so.. i hope this was the only nerf on him :D.

16/11/2010 :

Galio
* Idol of Durand
o Fixed a bug where casting would break an enemy's Spell Shield and then taunt them again
o Fixed a bug where the taunt particle sometimes played on targets that blocked the taunt
o Fixed a bug where Idol of Durand's ability power ratio was inconsistent
o Ability power ratio decreased to .8 from 0.85
* Bulwark duration reduced to 3.5 seconds from 4
* Righteous Gust base damage reduced to 65/110/155/200/245 from 70/115/160/205/250
* Righteous Gust ability power ratio reduced to 0.65 from 0.8
* Resolute Smite ability power ratio increased to 0.70 from 0.6