I'm going to post somewhat the opposite of what Kael said.
Never play bots, unless you really need to figure out a champion and can't be bothered to Dominion. Bots teach bad habits and you'll take a lot longer to get rid of them. Play a game of bots if you've never LoLed, then go straight into PvP. People are horrible all the way up; I'm at above 1800 Elo on Dominion and I still get barely functional quadrupal amputees.
Find a champion that fits your playing style
in every single role. Yes, including support. Yes, playing support in low-elo is, to quote Yahtzee, like hitting a wall with your fists, then going to the hospital to get them bandaged and then returning to hit the wall some more. And it's your wall. But you need to do it since you'll be stuck playing support a lot and you can actually influence the game as a support; either by helping your carry come out on top, by initiating (Blitz, Leona, Sona) or counter-initiating - mostly Sona, here. Never stick to one role, since there's about 50% chance you won't get to play it. The meta is there for a reason - if you don't understand how exactly to break it you should probably stick to it - it's not the best, but it's definitely the easiest way to play in low Elo.
The last-hitting and reading guides are excellent points. Get AD reds, they help with last hitting if you're having difficulties. On solomid read only featured guides if you can, they're generally written by pros. One thing, when you read guides try to figure out why the guides recommend items and builds, and when can you diverge from them. Blindly copying builds is the worst you can do.
Watch streams, watch
Studio's dailies on youtube - helpful stuff.
Don't buy T2 runes, buy some Tier 1, then save your IP for T3 runes cause that shit expensive. Buy the low-IP cost champions first, since there's rarely something you can do with a 6300 IP guy you can't do with a 3150. For example, Ashe and Corki are excellent low-IP carries, Nunu is a decent jungler, Udyr is a great jungler, Amumu works really well as an initiator, Ryze gets regular play mid and morgana is 1350, I believe? Soraka is great for support, Sona and Janna are very good too, Olaf is a great top, etc, etc.
And a general rule I always follow - play until you lose. If you're feeling cheeky, play until two losses in a row. Never play after that, because you get angry and being angry leads to sloppy play and POOF magic circle.