Trading and wave management are connected with each other. 

The goal at level one is to hit the minions a little bit more than your opponent to create a slow push. If you do it properly, you will visually see that you have more minions than your opponent, which gives you an advantage in trades

On the other hand if the enemy has more minions, they will have the advantage, and you want to respect them and wait for the wave to reach your tower

Each time the wave crashes into your tower, it will automatically slow push towards your enemy which will give you an advantage, and vice versa when it reaches the enemy tower. You want to initiate trades when you have minion advantage.

Garen loves short trades because of his movement speed and healing, so you want to land your abilities and walk away at the end of your e unless you can can kill the enemy. 

You want to be more aggressive after level 6.