Garen is, in my opinion, a very strong champion in dominion. His starting stats are phenomenal and the things that make him just an okay pick in normal don't matter as much here (mainly lack of cc).

This build is not for a tank. Garen sucks as a tank. He has 1.5 tanky abilities. Courage and his passive. Courage lasts 3 seconds. That is all the tanking you get. Not very impressive.

Demacian Justice is a great finisher. It is also a fantastic way to killsteal. Remember, you aren't the tank and when you get fed you become unstoppable.

I go 21/6/3 for my masteries. 1 point in cripple because exhaust rocks in dominion and why not make the enemy weaker? Everything else should be self-explanatory. I go for 3 in Good Hands to take the edge off that death timer when every second counts. You could instead run dodge and get nimbleness if they are running a lot of auto-attackers like Kog or Yi.

Garen is all Attack Damage. I run Armor Penetration Quints/reds because Flat AD runes don't really scale throughout the game. Armor yellows are pretty much a must, although dodge is a good choice against a team of auto attackers. Magic resist blues can be substituted for just about anything you want if they don't run much Ability Power (this tends to happen in dominion).

Exhaust because you want the slow in order to kill with Garen. Not to mention it is very handy to reduce their damage and resistances. Put it on a carry in a teamfight or to turn the tide of a 1v1.

Flash is a fantastic offensive and defensive spell. It is also great for getting in range with your ult and for flash spinning (great for making sure someone dies or spinning in the center of your enemies).

Ghost is a good offensive and defensive summoner spell that works well in Dominion. The added speed boost can help you get from A to B in enough time to halt a capture.

I really can't see many of the others as viable. Garrison is kind of a waste - this isn't a tank build so your survivability on the turret isn't amazing. You could argue it is great for diving, but your w lasts about as long as you should be diving. If you need the dive to last longer you probably needed a teammate.

Ignite is just inferior to exhaust. Dominion doesn't have a whole lot of champions escaping with 50 health (it does happen but it doesn't feel like you were robbed like it would in normal). The best use of ignite in Dominion is against champions that need to health up in combat (Yi, Warwick, etc).

Garen doesn't use mana so he doesn't need clarity.

Promote just seems like a waste. Someone tell me different.

Revive only comes up every 9 minutes. You might use this twice in a game of Dominion... but hopefully not because you are Garen

Heal - This isn't a game type where you can trick someone into overextending and then heal yourself for first blood. There aren't many minions to heal either.

There is no jungle with monsters to smite. This is a bigger waste than promote.

Your spin removes all slows so I don't bother with cleanse. Even with 21/6/3 masteries, you won't be squishy enough that your life is in serious jeopardy when rooted or stunned.

Spin to win is the name of the game. Judgement applies critical hits and what could be greater than being able to crit all your enemies at once? As the game progresses Judgement becomes less useful for damage and more useful for getting out of slows. If you aren't moving fast enough while spinning and you didn't use your Decisive Strike you can proc it now to speed up. It has the added benefit of being ready to do extra damage and silence (no flash for them) on your next hit and put them an ult away from the grim reaper.

Decisive strike is a must for finishing off enemies and silencing casters in your first fight. It also makes you run faster (very much needed on Garen).

I hold off on Courage till level 4 because you will hit level 4 DURING your first fight. If everything is going well you weren't even focused when the fight started. Keep an eye on your XP bar and dump a point in courage. If you lost a friendly champion or two you probably need this to either finish them off or get away without dying. It only works for 3 seconds and its cooldown is looooooooooooong; so use it when you really have their attention.

I usually like to keep my damage up and max Decisive strike first. If you find you keep getting left alone to guard towers or the enemy team is just melting faces, put an extra point or two in courage early.

Roughly speaking, Demacian Justice will finish someone off at 10%, 15% and 20% health based on its respective rank. One very crucial note: YOU CANNOT USE YOUR ULT WHILE SPINNING. I know this sucks if you were counting on it to finish someone off before you got finished off (you have no idea how many times that has happened to me). You can, however, queue up your ult while spinning and even as the enemy pulls away from you it will still finish them.

This is my core build for every match. I usually start with prospectors blade for the 200 health and 20 damage. It is basically a ruby crystal and a pickaxe for 500 less gold. You have to have boots in dominion or you will be too late to the party on top. I grab a health potion because it has made the difference in enough teamfights over the windmill than I can count. Chug it as soon as you start taking damage, put a point in Courage as you level and win the teamfight because they shouldn't have focused you off the bat. Worst case you have to pull back and re-enter the fight, possibly after grabbing the healthpack (try to save that for a dying carry unless things got dire for you).

I tend to finish boots next because I need the movement speed. There are no other boots for Garen. If you run any 2 speed boots you will be too slow and will be easily kited. Trust me, I've tried. If you need tenacity grab Cloak and Dagger. If it's magic resist you need get a negatron cloak and build it into a quicksilver sash or force of nature.

Inifity edge is core and its is first. Garen's damage does not scale well throughout the game on its own. We need the crit chance, we need the damage and we need the extra crit damage. If you don't have the money for the B.F. Sword get the Cloak first. The damage from crits as you spin is worth more than the pickaxe's damage.

Phantom Dancer gets our crit chance way up there. More importantly it increases our run speed. Less importantly but very much needed is the attack speed. Garen's auto-attack is painfully slow and at this point in the game you aren't killing with a Decisive Strike and a spin of Justice.

I've honestly never really played a game that went on long enough where I didn't need a situational item so I can't really say what would be core after this. Late game you will be auto-attacking more and more. But I can't speak for your team comp. If you are needed more as a tank then you may have to build in that direction. If you need to tank AD and could use more damage/crit Atma's Impaler is a great choice on Garen. Sprit visage is also a good choice and it is cheap! Magic resist, 10% Cooldown Reduction and an increase to our passive health regen (such that it is almost on par with a Force of Nature).

Sword of the Divine - You shouldn't be wasting a ban on Jax. He is too easy to counter with this one item. The attack speed on Sword of the Divine is much needed on mid-to-late-game Garen and the armor pen on proc is just fantastic. Oh, I almost forgot - 100 damage every 4th attack never hurt anybody either (unless they were on the business end of your sword).

Thornmail - AD carries love my Thornmail.

Force of Nature - For very heavy AP teams. Works great if you build Atma's Impaler and Spirit Visage. Lots of health, lots of regen, and lots of damage on Garen.

Quicksilver Sash - Get rid of pesky roots, stuns, blinds and a decent chunk of the magic damage which come with most casters.

Cloak and Dagger - Crit and Tenacity, fantastic.

Things I don't run:
Lifesteal - Garen doesn't attack fast enough.
AP - Garen doesn't do any.
CDR - I don't go out of my way to get cooldown reduction. Sure, it is nice to have. But you don't really need your spin as much late-game and Courage has too long of a cooldown to use twice in a fight.