How do I know if I have brittle bones?

DEXA. But may be un-necessary, dexa is the standard test for osteoporosis. Unless there is an underlying reason for a suspicion of brittle bones, i'd avoid the test until you are post menopausal (for females) or even older for males. Its expense and radiation for fairly low yield.
Frequent fractures. People who suffered from brittle bones will have a higher incidence of fractures that occurr after minimal stress or trauma. Ask your doctor if this is a recurring theme.