Firstly it is important to point out around 9 out of 10 lumps and bumps are not cancerous, but some are, so getting them checked early by a doctor is a good idea. Remember that males have breast tissue too so can get breast cancer, but is much less common.
Breast cancer is the most common cancer in females in the UK with almost 50,000 cases diagnosed each year. Although it is the most commonly diagnosed cancer in women under 40, 81% of cases of breast cancer are diagnosed in women over the age of 50.
How to self-examine:
Choose a time when you are relaxed and comfortable for example in bed, the bath or shower. Avoid examining your breasts in the week before your periods as they are commonly sore or a bit lumpy and this is normal. Ideally, check them once a month.
Begin by looking at your breasts in the mirror with your shoulders straight and your arms on your hips. Note any change in appearance in the outline or shape of the breast, especially those caused by arm movements. Note any changes to the skin such as dimpling.
Using your right hand to feel your left breast and then your left hand to feel your right breast – keep the fingers flat and together, use a firm, small circular motion to feel over the whole breast, including the armpit. Note any discomfort or pain in one breast that is different from normal. Feel for any lumps, thickening or bumpy areas in one breast or armpit which seem to be different from the same part of the other breast and armpit. Note any discharge from the nipple, new for you or any other changes to the nipple such as it being pulled in or pointing differently or a rash over the nipple.
More information here.
A great video showing how it is done is here.