Garen is a very easy champ, and very versatile. Even though it appears as more tank than damage, that depends on your playstyle. Depending on your team composition needs you can choose which aspects of Garen to use. You can complement it's passive and stats building tanky, and being nearly inmortal. Or you can make super damage and one shot Q. Or play moderately and flexibely. Over time you learn how to build yourself considering matchups and team comps.

Usually Garen get's countered by ranged champions, but even then you can try to Q-E-R him and kill him. Usually when I play again a squishy champ, I hide in a bush and let it push, then it's a free kill. This strategy may not work with melee matchups. In these ocations, if the matchup is an easy one, like Jax, you can try to deny as much farm and xp as possible. If it's a tough matchup, like Tryndamere, you may wanna freeze or farm under tower. Early Garen is not a good turret destroyer, so perhaps instead of pushing you may wanna help in a Herald after a kill or back.

You can either be the damage source or the damage absorption of the team. So, you should try to be with the team when a important moment arrives. The rest of the time you should try to farm, with no much worries. Garen can 1v2 or even 1v3 almost every champ if fed. If you aren't fed, you should try not to die and to get as much farm and kills as possible, going with another teammate.

This is the part of Garen that is not very complicated. You can just Q-E the enemy, give some AA and W when they are going to throw an abilitie. You should try to give as much damage as possible with the E, and take advantage of the AA reset of the Q. The R should be thrown at 33% life of the enemy, the less the safer.