Time is the best medicine. Just try to not think about it. 

It's impossible to forget someone completely, as their memories stay with us forever. But all I can say to you is that whoever that person was, they were not meant to stay forever with you :) They were to leave one day. You keep one thing in mind and that is, before that person came in your life- you were living without them. If you could do that then, then you can do that now. Everything happens for a reason! Good luck ^_^

Depending on relationship, sometimes it is impossible to forget.  I lost my only child to cancer, telling me to forget her is like telling the sky not to turn blue.  Impossible!  When you are in so much pain because you can not forget.....turn to your inner strength and your faith. Thank God/Allah or what ever higher power you believe in that you at least had the time you did with that person, because though you may not see it now, you learned you are stronger than you thought and in time you will see, if this person left you, they were not good enough for you from the beginning.   :)

If you really have to say goodbye, the best thing to do is to erase all traces of them from your life. If you think about them, you're apt to hurt yourself again. You have to rebuild yourself without them in it, and the only way to do that is to stop thinking about them, to stop thinking you can rely on them like you used to.

Thanks for the comments everyone! I appreciate everyone's feedback :)