For starters i would recommend you to play AD Carry Champion types.
For example this weeks free champions are Corki and Draven - ad carries.
U ussualy play them in so called "bottom lane".
Try to focus on killing minions by last hitting them with ur basic attack (right click) when they are on low Health.
That way u wont push ur lane too much so u can stay near ur tower and be more safe.
Thats how i was doing it when i started playing LoL.
Practice one type of champs for a start so u can get a feeling how it should be played.
Also, do a tutorial in-game and look on other tutorials on sites.