By learning the enemy, it helps by knowing how all the champions work and play, so when a champion is free to play for the week, give them a shot so you know what you might be up against in the future. A lot of game time is needed to go through and play all the champions, over time you just know how they all work and what to do about beating them.
The best way to get early advantage in a game is to try to get to level 2 before them and try to kill them then or get level 6 first. This can vary on the champion you are using, but most of the time it is best to fight if you are the level advantage on them. Item advantage is the other big factor in this, it is always best to keep track on what your opponent is buying and building into and knowing how much stronger they will be with that item.