start off with the boots of speed. You wont need potions for this. You have heal and Garen's passive. Next you have to get a last whisper. Follow it with the guardian angel. The decisions are made here you can get a sun-fire cape or an aegis of the legion. If you choose the cape, your next item will be another last whisper and then you can buy a frozen mallet. If you chose the aegis, you will get a frozen mallet and then a black cleaver.

I can play Garen in mid quite well. This requires you to play offensive to get a killing spree early on. I usually get 3/0 in the first 15 minutes. Decisive Strike on a turret will knock it down a bit. You should play hit and run with the turret like this until it is down. If there is more than one enemy mid, back up to your turret and taunt them with Judgement. Use Judgement to swing out at them and fall back to the turret. This should cause them to attack you and your turret will then attack them.