A few tips:
Early game, minions do a lot of damage to you. So, if you attack an enemy Champion, you draw the aggro of the minions, which hurts.
Early game is all about sustaining and last hitting minions. Build that gold up to buy better items for bigger stat advantages against your enemy.
You mentioned switching lanes "too much." That's not really a bad thing. Sometimes waves of minions build up, and you need to go farm them before they take our your towers. Especially if you were down a man like you said, you'll need to rotate lanes. I generally push my lane into the enemy tower early on, then roam to another lane to help gank the enemy to help my teammates who are struggling. There's also "split-pushing" which you'll learn about later. But, that involves a lot of lane hopping and pushing.
As for Garen, I usually start with one point in his Q. His Q silences enemies and it gives him a movement speed boost. So, you can use it to last hit minions, silence/damage the enemy champion, and use it as a gap closer or an escape. Then, with 1 point in Q, start maxing E. E is where you do all of your major damage. I'd get a single point in your W after you get 2 points in your E. W mitigates damages, so it's really nice if you time it right.
Just stick with Players vs Bots for now. Once you've got your feet under you, then go into PvP.