It's hard to start out at times. When I started a few years ago there was a lot less champions available. Best idea is that in bot games, the AI is pretty derpy. They're also great to learn and practice vs.
As a core thing, take advantage of the free week times to try out each champion. There's basically tanks, support, magic DPS and melee DPS. Try to find one of each that you like, and play around with them.
The biggest thing I can say, map awareness. With standard setups being two bottom, one mid, and two top (Or one top and one jungling). You need to be aware at all times where your team is, where YOU are, and where the AI is. If you're out pushing their tower and your not seeing an enemy, be wary. Don't over-extend to try and kill that tower, or rush into three people to kill one, it's not worth it.
League of Legends #2 - Ranked Dominion - UrgotThat is a replay of mine playing dominion. The gameplay is different, but the basic idea of gameplay is the same, over-extending, learning your character and such as well as seeing how I screwed up. (I'm Veronath).
In dominion you try to hold 5 capture points. The more you hold, the more points the enemy team looses.
I rarely play anymore, not that appealing to me much these days however it's a lot of fun once you get the basics down. Guides are ok, but better to watch a video of the character in action to SEE how their moves work.
Cheers.