Everyone has a past and sometimes that past can come back to haunt him as his ex-girlfriend. Try as you might, you cannot erase your boyfriend's past. Therefore, the only option left is to learn to deal with your boyfriend's ex.
Talk to your boyfriend about his ex. Ask him what were the reasons for the break-up and how he feels about her now. Try to be sensitive to his feelings about this person. If he does not want to talk about it, do not press the issue.
Ask his friends about the ex-girlfriend and her relationship with your boyfriend. Friends can be a better source of information because they can have some perspective about how the previous relationship evolved and eventually ended. Understand that he may still have a relationship with the ex-girlfriend and his perspective may be biased.
Be confident in yourself and your relationship. If you becomes too worried about an ex, it can hurt the present relationship. Know that he is in a relationship with you now. Investigate the ex if she is a problem, but do not obsess over her.
Contact friends of yours about the situation and ask for their input. While your friends probably did not know the ex-girlfriend they can be a means of support in dealing with the ex.
Speak to the ex-girlfriend directly about how you feel about her. This is probably the riskiest means of dealing with the ex-girlfriend. This could possibly make the situation worse and end in confrontation. Just remember to be courteous and respectful when talking to this person.
Seek counseling if it becomes too much of a problem. An impartial observer can really help you work through your feelings about a personal issue.
Get a restraining order. This is the last viable step, but sometimes an ex-girlfriend can get out of control and you may need to contact the authorities. Do not enter into this lightly, because it can put undue stress on your life.