Your Win Condition
This is a classic counter to Jax. Your primary goal is to establish a lead between levels 1-6 to survive the mid-game. If you can go 0/0 in lane, you are winning.
General Strategy
Try to counterstrike Garen's empowered q. Your counterstrike reduces aoe damage so it also reduces Garen's e damage by a little bit. Do not face tank Garen's e especially if its only hitting you. Garen's spin does more damage to the nearest target. If you are both even he can kill you from 50-70% health pretty reliably with his full combo and ignite. Garen is vulnerable to jungle ganks with limited mobility and often lacking teleport. Garen is also weaker than you in 2v2 or 3v3 skirmishes around rift herald where the fights are drawn out.
Trading Patterns
Pre 6 you can stack your passive on the wave and try to bait out Garen's w or e. If Garen doesn’t have cooldowns up and you have stacks on your passive you can look to fight. After 6 Garen has a lot more kill pressure on you. You either have to all in Garen at full health when his w or e is down or take one auto trades with w. Taking multiple heavy trades with Garen hard favors Garen. Garen wants to trade on his e and w cooldowns. His optimal trade on you is spinning and using his w to reduce the counterstrike stun and walking away from you. In the early game this trade will be around even, but Garen can sit back for a while and let his passive sustain him back up. If you are even, after berserker greaves, Garen needs around two trades to have kill pressure on you with his eqr ignite combo. If you are behind then, Garen only needs one trade with his e to have kill pressure on you.
Wave Management
You always want the wave near your turret in this matchup. Early on you can look to slow push the first and second waves and fast push the third wave then either cheater recall, get vision, or rotate. If you cheater recall, you have to try to thin the wave and look to freeze on Garen with your item advantage and stacks on your passive. If this fails and Garen gets the shove to your turret, slow pushing the wave back to him should be fine. When you are slow pushing back to him, you should avoid fighting him when he comes back with berserker greaves especially if he is close to level six.
Their Win Condition
Garen wants to scale up to his berserker greaves and then look for heavy trades onto you. He will always want the wave on his side so that he can take short trades with his e. Wave management