Breast self examination has long been one of the methods of screening for breast cancer, by trying to find cancerous lumps at a time that they are more amenable to treatment. Other methods include breast examination by a clinician and mammography. The exact combination of screening methods that works best is still a matter of debate and the appropriate scheduling will vary from woman to woman based on individual and family history. Therefore, it is recommended that women discuss with their health care providers if they should be doing monthly breast self-exams or at least some breast exams to familiarize themselves with their breasts.
If a woman is advised to do such examinations, the time she is preparing for the mikveh is very appropriate. Mikveh use is generally at a consistent time of the menstrual cycle, she is undressed and inspecting her body anyway, and a mirror is usually available.
A breast self-exam is done in two steps. The first is to stand in front of a mirror with hands on the hips and observe the breasts for any change from the last examination as well as any striking difference between the sides (no one is perfectly symmetrical). The next step is to palpate (feel) the breasts in a consistent and thorough fashion, checking for any lumps. The most common recommendations are either in a circular motion progressing from the chest wall to the nipple, or going from chest wall to nipple as in the spokes of a wheel. If she finds a lump, or feels anything on one side that she does not feel on the other, she should consult her physician. Most such lumps are benign, but they should be checked to make sure. It is not unusual to have changes in the breasts during pregnancy and breastfeeding.
You can find more detailed instructions online. One good site is http://www.breastcancer.org/symptoms/testing/types/self_exam/bse_steps.jsp.