Having been a babysitter in NYC, I can tell you that the customary thing to do is guarantee a min of three hours per babysitting job. If don't use them for that long of a time then you still pay them for the three hours.
Are you hiring this person to come for a set schedule? (i.e Mon, Tues, Wed, from 3 PM - 6 PM) Or are you hiring this person for days/evenings and weekends as you need them? If it's not a set schedule the only thing I recommend is canceling at least 24 hours in advance so that they can accept another job. The earlier the better in this case, especially if she babysits for other families. If you cancel them last minute it's always nice to pay them at least the three hour min. If it's a set schedule and you feel that there are times you won't need them, then I would recommend setting up a time limit for giving them advanced notice right from the beginning. I would say that if you work out a bi-weekly or monthly schedule in advance this will benefit both you and your babysitter. This way they can work their schedule around yours, and it works out for both parties.
Your babysitter might also have a set requirement. It's always nice to communicate these things from the beginning so ask them before you bring them on board.