You can always check online or in the yellow pages under "Furniture: Repair, Refinish or Restore." However, get professional references when possible. Check with furniture stores, interior designers or antique dealers. Staff members at historical houses and museums can often recommend restorers.
It's a good idea to visit the workshops of prospective refinishers to see firsthand some of their work. Any reputable refinisher should give you a free consultation and an estimate of the cost to repair.