There are a lot of great Garen guides, where you can read about how to play well. I learned from those builds (especially "Garen - Spin to Crit" by Palthios) and after about 500 games with Garen I don't have nearly nothing to add about game style. The only really important thing I would like to enhance is the items build, but there will be some of my thougts about other aspects of game as well.

Garen, even if ad, is not ad carry. Your role in the team is to own solotop, so enemy solotoper (or top lane in case of 1v2 top) will be weak. Playing bot can be also effective, but only with good lane partners. Garen deals unbeliveable damage but only in early game. Most of the builds are trying to either take advantage of it or ignore it. This is simply bad. In the first case (building dps), you are going to build infinity, which can be bought, let say, at 25:00. You will see your damage increased greatly after buying bf sword, but then infinity make no big difference. Of course, your attack will be much stronger, but enemies have too much hp at this point. You go teamfight, compare your damage with vayne, teemo, tryndamere, (type your favourite ad or ap carry) and the only thing you can do is b, [enter], /cry.

On the other hand, Garen is great tank late game. But if you are going to tank from the beginning, you will never make any damage and enemy will simply ignore you. No taunts, no dashes, no damage. It is nice to have the possibility to take tons of damage, but no one serious will ever attack you!

My idea is really simple - to combine two builds and create true "OFFtank", who will own early game and weaken his enemy (enemies) seriously, and then tank well still being dangerous.

These are quite obvious and copied from other builds. The main idea is simple: enhance your attack damage in early game. You can even go 29/0/1 in masteries, if you want, it doesn't matter so much. Also Seal and Glyph runes are not so important. If you like, you can change them to armor/magic resist per level or whatever you want. You only care to maximize apen, or apen + ad (flat, because you want to own early).

Skill sequence is also obvious and copied. Kill enemies with q + e + r, using w whenever you need. Later, the shield skill will be more important and then it will be maxed.

Flash + exhoust is absolutely best option. With this spells, you gain much escapeabilty and possibility to chase enemy or even tower dive. You will probably sometime miss Ignite, but, well, r is quite nice finisher, isn't it?

This is the main part of this guide.

Early game: destroy your opponent
Starting with 3 Doran's blade gives you massive ad boost. The faster you get these, the more early kills you gain. But still, buy items wisely: if you must return at ~350gold, buy boots, when you come back to base, you will probably have enaugh money to buy next 2 doran's. Some hp pots and sometimes wards are very good idea.
3 doran's are important for one more reason: with ad masteries and runes, they let you farm easily with e (with some luck, you will kill all minions in a wave with single e + q for that big minion).

Boots:
Of course, boots are not so important, but with Mercury's Treads you gain magic resit (remember you are going to tank soon!) and tenacity which is always good.

Mid and late game: judgment is not so op now
At this point, you still deal nice damage, but not so good as other champions. If so, go ahead and make advantage of your tanking ability. The best order is: Warmog's -> Atma -> Force of Nature -> Thornmail. But, of course, not every game you should do that. It is the best, because after some tanking (Warmog's), you build Atma so your damage is decent again. Then FoN and tons of hpregen (about 350 with passive) let u stay under the turret for hours, fight enemies, then hide in the bush for couple of seconds and attack with lots of hp while no one expect. But, obviously, you want to change this order if there is fed enemy ad or ap carry. You can also buy Randuin's Omen instead of Thornmail, if there enemy team is high ap.

The last item is your choice. I play so little games which allows me to buy it, that I'm just too inexperienced to give any advice. Personally, I would buy Guardian Angel, which is always nice as last ;)

This way you are useful for whole game. If early was exciting with your recent build, it will be still as good as it was, but now in the mid and late game nobody will ignore you, so you can take huge damage, bo back for 10 secs and fight again. And you even do some nice damage!

Remember, that this is not your main guide. It is only extension, a set of advices rather than complete howto. Read other highly rated guids on this site to learn how to play Garen and use this one only to modify some details of your build and gamestyle.