A family history of breast and ovarian cancer, particularly at a young age, is one thing to look for. This is the first step. Next, have this confirmed, preferably at a familial cancer clinic, by a trained geneticist. These clinics are available at most university medical centers. Because this is so complicated and costly, most physicians rely upon strong family history as a marker and few women actually choose genetic testing.
Some genetic predispositions are more common in particular ethnic groups.
Your physician can give you more information, and there is additional information on the Web. I've read about new types of mammograms. The new machines are more sensitive. There are experimental studies going on with magnetic resonance imaging and other modalities. Someday it may be possible to get earlier diagnosis with less pain.