You should continue to play normal games. Here's what I tell most people:
Become aware of every role. Play all the roles, top, mid, jungle, support, ADC. This will give you an idea of what each role deals with. Once you go through each (which you could've done in the grind to 30), you want to pick a handful of champions within that role that you LOVE playing. I'd say two or three at most. Master these champions, read up anything you can on them and get good at these champions, this will get you far (and you'll have fun doing it in the process).
You also need to learn how to last hit. With the champions you like, open up a custom game and play without runes or masteries for 10 minutes, with or without bots, with no items. Attempt to get the killing blow on the minions in your lane, and aim to get 100 creep score by the 10 minute mark, that's the perfect score I believe.
For runes and masteries, good choices are: Armor, MR, Health, and AP/AD. These are good runes to have, but if you know what champions you enjoy playing, here: http://champion.gg/
Click on the champion you like and the role (if they have multiple positions they can fill), and focus on getting the runes there. The runes pulled from this site are from plat ranking and higher, so they are generally a good idea to start out. Masteries are also in there, as well as what people build item wise and what skills they level. Outside of that, searching for guides on the champions you enjoy will also give you bunch of different perspectives.
Anything outside of that is general advice: Dragon, Towers, Inhibs are more important than kills, generally. Towers give team gold, Dragon gives team wide boost, blah blah, objectives are important. You'll pick up on this over time, but so long as you do everything before this paragraph, you'll be fine so long as you keep playing.
Good luck.
