Wave Control Help Please

As a jungle main(support secondary), I don't play a solo lane or carry role very often, but when I do, I don't know what to do with the minions. I know I'm supposed to kill them for gold(I think), but how fast do I want to kill them, and how can I kill them when my team wants to group?

Okay, enough playing dumb, but seriously guys, I need help understanding how/when to push, when/where to freeze, and when to set a slow push. I know that slow pushes deny my team CS and build huge waves for the enemy to farm, but I also know that there are uses to doing it. Also, any other information related to controlling minions in lane that you want to provide would be greatly appreciated.