Riot sometimes links videos on how to get better: http://na.leagueoflegends.com/en/news/community/community-spotlight/catch-climb
I'd say in general if you play top, mid, or adc be able to last hit. If you play jungle know what route you want to take for clears and when it's a good time to try and gank. If you play support know how to lock down enemies with CC or how to peel or heal and where to ward.
if you look on youtube Foxdrop has some good videos for getting better, Gbay99 had some really good tips on getting better but his newer videos focus on other things.
If you watch streamers on twitch Nightblue3 gives lots of tips for junglers and tells you his logic for why he is building the way he is building during his games so if you want to watch some of his past streams for insights here is a link to that http://www.twitch.tv/nightblue3/profile
Other then that I'd say just try to play safe when you first start doing pvp games and see if you can ease your way into them by playing with some friends.