How old should a female when she should start getting mammograms to check for breast cancer?

Depends. In the absence of a family history of breast cancer, the american cancer society recommends annual screening mammography starting at the age of 40. This should be performed in conjunction with an annual clinical breast exam by the patient's doctor. A self breast exam is also recommended.
Usually 40. Does depend on specific situation. For the general population, 40 is usually accepted. If there are symptoms, it can be done earlier. If there is a strong family history or known brca mutation, should start earlier, usually 10 years before the date of diagnosis of first family member w/ cancer.