You get experience points for winning (2) or losing (1) fights you initiate with opponents as least as high as 2 levels below you.
The best strategy is to pick opponents 2 levels below who don't have a bear or something else awesome.
You also get experience points for a new pupil and then each time that pupil levels up.
Here is the kicker: only one pupil per IP.
Since you can only fight 3x per day (max 6 experience points per day from fighting), the trick is to get pupils that are going to keep playing and level up.