So, I'm just a mid Silver, so take what I say with a grain of salt. But I mained Garen in S5, and I got more than 150 games with him in ranked.
If you play against him, you have different choices:
- you play a champion that can really dominate him by constant poke (Gnar, Vayne, maybe Vlad) and you just outfarm him by zoning him and freezing the lane. In that case,
is a good first item, for even bigger poke (not with Vlad, obviously ;)).
- you play an even bigger lane bully than him (Darius, Renekton, ...). Once again, your goal is to outfarm him by zoning him, but in that case, it's pretty much a skill match-up. You need to know the proper skill rotations to get favorable trades (see example with Darius in the end). Generally, it's better to build defense first and just farm. If you build offense and try to fight (which seems logical if you are a bigger bully), a good Garen will simply refuse to fight and freeze the lane just before his tower thanks to his spin which is a great skill for wave-clear.
- you can't dominate him (and your purpose is to be more useful than him later in the game) and you just try your best to farm. Accept that you will be slightly behind him in farm, and no worries, that is OKAY.
The single biggest mistake you can do against a Garen is trying to kill him. Against a decent player, it's impossible to kill a Garen in lane. Your aim is not to kill him, it's just to not get him fed. Your simple presence will prevent him from free-farming, and if you don't die, he won't get ahead. Whereas if you try to kill him and fail, he will get ahead, take your tower, then roam and snowball other lanes. Don't take the risk to fail. Farm.
For the third case, it can be slightly frustrating/depressing, but you need to keep your eyes on the long-term objectives.
- If Garen doesn't push, don't blame your jungler if he doesn't come to help you but he is doing something useful somewhere else. Just farm the best you can. Remember Garen only brings one thing to the table: DAMAGES. If you don't give him kills, the gold he gets just with farm is not enough to carry the game by itself. And if he doesn't push you under your tower, you should be able to stay even in farm with him, and just wait for the late game.
- IF he pushes you under tower, then call your jungler. Remember: it's YOUR responsibility to set-up good gank opportunities for your jungler. If you push, or if the lane is frozen in the middle, your jungler would just waste time trying to help you.
Quick example about bully vs bully trades with Darius:
- if Darius misses a grab, Garen just run to him, use the spin, silence with Q then runs back, and Garen won the trade.
- if Darius connect the grab, Garen spin to his face, Q then runs back --> even trade
- the good move is to keep the grab as a threat and farm. As long as you have your grab available, Garen can't fight. If he tries to fight, wait for him to use his DPS, and when his skills are on cooldown and he wants to retreat, then grab him back, apply 1 or 2 more stacks of Darius passive and Q him when he finally retreats. Congratz, you just won a massive trade.
The trades are different for every single match-up, and there is no miracle, you need to learn them by yourself. With Renekton, you should keep your Fury up, and punish Garen if he uses his skills to farm, but just back if he tries to aggro you first.
Hope that helps :)