Sims 3 Witch , How to make her learn faster ?

The spellcasting duels with other witches helps raise it quite a bit. Witches are SLOW to level. I haven't tried, but if you have university, you could try holding a protest and if it's successful you'll get increased learning (or whatever it's called) and that might or might not help to level the skill faster, too.

Successful protests help level skills faster, I'm just not sure about the witch skill. But once you get to the mid to high levels, the playing with magic is a slow, painful process to level with.