Not a Garen main but..... Adaptive Helm and Spirit Visage will just about nullify his threat unless he is AD. If he is AD then build Visage and just get Thornmail next. His magic damage is much more potent than the autos until he gets Bork and hurricane etc so the armor isnt needed until 2nd item.
Dont try to be too aggressive if they are a gentle teemo. If they start something trade back harder, but if they want to passively farm do so. Just means you will out scale him and your jungler can deal with other lanes.
If they are aggressive, try to trade level 2-3 if the opportunity arises. This will either
A) turn them passive.
B) make them more aggressive and an easy easy gank.
If they lose the trade they will likely be more passive, because they do not want to risk another trade loss..... if they win the trade they will attempt to shove theor advantage by extending past their minions and yours to try and make you lose CS and experience. At this time it is an easy gank until he is level 6. After that, red trinket will be your friend and partner. Your job will be to clear as many of the mushrooms as safely as you can. It is a heavy drain on his mana to place those shrooms and after a Spectral Cowl they will barely tickle.
Adaptive Helm will make that even more so tickling because the first tick will lower the damage of all the rest. Visage next will bump up your Passive which by then you should be level 11.... and the rest will be for your lieasure and luxury.