In reply to Murcantile:
Not a medical opinion but I have suffered three significant finger injuries over my climbing career. In each case, I waited a minimum of two to three months before climbing and then took it very easy, climbing on larger holds for a further month or so while I strengthened the affected joint, ligaments and connective tissue. After six months, the fingers were back to normal.
Hot and cold treatments are useful to improve blood flow to the affected area, which will speed up healing. If you have only very recently injured your finger, follow RICE - Rest, Ice, Compression and Elevation (to reduce swelling). After the initial inflammation has reduced - possibly a few weeks or more depending on the injury - you can start to gently massage the tissue around the area and start to gently stretch the joint. Over time, this will help reduce the build-up of scar tissue and alleviate the stiffness that this can cause.
Obviously, as others have already said, see a physio or soft tissue therapist for their advice. If you are in pain also get it checked out by your GP.
As a final point, do not stress about not being able to climb. The finger will heal and you'll be back to it in no time. Who knows, the break might even do you good!