How much of my tooth will they have to fill if it's broken?

All that is damaged: Your dentist will need to clean out as much of the tooth that is necessary so that only the good, solid part of the tooth remains. Can't tell what the condition of your tooth is so you will need to ask your dentist.

Depends: Usually teeth break due to an underlying cause. Most common is tooth decay followed by a poor bite. If decay is the problem, the amount determines the size and type of restoration your dentist will use. Small decay, small filling. Massive decay, larger filling, maybe root canal, and possibly a crown!