As a new player, playing unfamiliar enemies is a pain! Here's my suggestion to reduce headaches.
Coming from Dota, it's really hard to be stuck with having no clue what all the characters are capable of all over again. The problem is, I have to either deal with trying to figure out the enemies' abilities by eye, or I have to tab out of the game and leave my team on their own while I look up the champ's abilities.
Dota had a feature where you could just click on an enemy hero(champ) and read their abilities by mousing over them, just like you were controlling that hero. All it told you was the regular description and the stats per level, it wouldn't tell you the enemy's actual level. So there was no special info you could get through it, just the same things you could get out of a wiki page without the hassle. I made a little mockup of how this could look in-game if a similar feature was implemented into League. (I couldn't actually show the skill tooltip, because I don't have Nasus. A singleplayer bot match to test drive champs you don't own would be nice!)
http://i.imgur.com/DRVdQuC.png
Here's an example of how the enemy ability information is presented in Dota:
http://i.imgur.com/akR3a4C.png
The information is presented just like if you were playing the hero, except you don't get to see their skill level. No more information than a wiki would give you, but it's a huge help for new players like me. (Or veteran players who are up against a new hero!)