Of course "Fluffy" is a valued part of the family. So how do you go about choosing a competent person to groom her?
It takes lots of careful handling to properly groom a dog, not to mention the precautions required around dangerous, sharp implements like scissors and electric clippers? A dog (or cat) groomer will be bathing you pet in soapy water and rinsing thoroughly. We surely aren't going to trust her to "just anybody".
Every time a dog leaves the groomer, it is a walking advertisement. Talk to your veterinarian, your kennel manager, your neighbour. If you see a dog on the street with a style you like, stop the owner and ask where the dog was groomed. People are usually very willing to talk about their pets, especially their new "do".
Some veterinary offices have policies not to refer clients to any certain groomer or breeder. Don't despair; ask more specific questions like "Have you treated any problems from this groomer, such as cuts or clipper abrasions? Have you had any complaints about this groomer?"
Did you go to grooming school or apprentice with a professional groomer? How long have you been grooming? Do you have much experience with (insert your breed here)? Do you have a problem putting poodle feet on a cocker? (Or some other non-standard clip?) Are you a member of any professional grooming organization? There is a national organization called National Dog Groomers of America Association and many states have their own groomers' organizations.
Some states require that groomers are licensed and certified in flea/tick applications. So ask if she or he is properly certified.
Keep in mind that groomers are usually on an extremely tight schedule. Ask him/her if they would be able to call you back to answer these questions when they have ample time to talk. It's hard to answer questions while fluff drying a dog. You should be able to develop a rapport with the potential groomer that will give you an overall impression. Hopefully it will be a good impression.
Just by asking around you will be able find answers to most of your questions. Using a groomer for the first time can be a disconcerting experience. If you've done some research by asking around and then place your trust in your groomer and then see a good result ... then you can pamper yourself, too, like "Fluffy" was pampered.