Take the lock apart, push it out and put it back together again.
Carefully Araldite a piece of wire to the broken part of the key and let it go off, pull it out.
Ive been able to grab it with small long now pliers and/or tweezers.
See if you can find a blade from a small coping saw or similar, slide it in the bottom of the key (teeth facing inwards) and pull it out. the key should (might) come out. A spray of wd40 helps.
Turn a small drill bit into and next the broken key until about an inch in. Pull the bit out and the key should start to come out.
Call a locksmith.
Theres different ways. You havnt stated what type of lock/key it is. that would help.