Not Updated For Current Season
Early Game: First off, to become ridiculous with Garren you need to remember one very important fact. You are NOT impossible to kill level 1. You should sit back and farm kills as able. Do NOT Rambo. If you are doing good then by 15 minutes into the game you will have both Force of Nature and your Ninja Boots. Just remember, Call MIA and only perform ganks / risky maneuvers if you are sure you will get a kill from them. Also remember your spin is an incredible destructive force at the beginning of the game.
Mid-Game: You should now have Force of Nature and Ninja boots, these will allow you to chase people using your Q, this gives you increased movement speed. Remember to use your W as a shield to stop from taking damage when initiating in large team fights. With your W active you should be able to enter into a 5v5 battle as the initiator and walk out, hopefully with a kill. Use your ultimate to steal kills, (Yes this s a ****-Move, however it will allow you to gain equipment fast which will benefit the team greatly).
Late-Game: You should be almost impossible to kill. If you die you either have A: a bad team, B: you were stupid, or C: You did not farm enough minion / hero kills so you do not have enough gear.
Have fun, and remember, Garren is OP, abuse it :D.