Start with champs that are clearly defined and low risk high reward. Such as the list below.
These champs are both safe and strong. Only play 3-4 champs to start, learn them, and SLOWLY expand your champion pool.
Healers: Nami
Enchanters: Janna and Lulu
Mages: Morgana and Karma
Engage Tanks: Nautalis and Leona
Defensive Tanks: Braum
The next part is a general description of positioning, but no where near definitive. You'll figure t out through play.
Positioning is everything, even with tanks. You don't want to stand on top of your ADC, but you need to be able to do your job. Healers and enchanters more behind the ADC, mages even with the ADC, and tanks slightly forward of the ADC. Always try to keep your minion wave between you and the the enemy until you are ready to engage, and then do so without showing your intent to engage.
Learn to Itemize, outside of your Sisghtstone item, you will need to figure out how to build to your strengths and weaknesses, and your opponents strengths and weaknesses.