If there is ovarian cancer on my dad's side, what chance will I have to have it?

Depends. One case? Two? Ten? Any other cancers like breast, colon, endometrial? Discuss this with your gyn to see if you need a consultation with a genetic counselor.
Usually low. If your dad's mother had ovarian cancer, particularly if at a young age and with other relatives having breast cancer, then your dad could have a breast-ovarian cancer (brca) gene mutation, with a 5% lifetime risk for male breast cancer. His children would have a 50% chance to inherit the brca mutation if he had it, confering a 50% lifetime risk for ovarian and 85% for breast cancer for daughters.