"What is a grace period, and how long is mine?"
If your payments are due on the 1st of each month, that is obviously when the lender expects to receive payment. However you will typically not incur any late charges until your payment is a certain number of days late.
Generally the grace period on a loan is 10 to 15 days before incurring a late charge, however this will not effect your credit scoring until you are 30 days late. Check with your lender for their exact grace periods.