Capstar is nonprescription. You can actually buy it yourself, but it should be cheaper from a vet or groomer (since you only need one dose, and the packs start at six doses). It starts working within 30 minutes and kills all fleas within four hours, and it's very safe. The only reason it's not used by every human being on earth is that it only lasts 24 hours--it's a quick knock-down, but if you wanted to use it to control fleas on animals that had any contact with the outside you'd need to give one every day. So it's really best suited to the times when you just want to make sure that every single flea on the cat or dog is gone.
Frontline takes 24-ish hours to work, and doesn't work very well at all if the animal is freshly washed. Frontline says it works after a bath, but I have found that to be untrue at least when it comes to ticks. I'll have total success against ticks until the dogs get bathed, and then I'll find multiple ticks on them every day. I personally think Frontline is awesome, but it does have its limitations.
If you can't get Capstar, I would give Frontline to the owner and ask him or her to apply it at least 24 hours before the groomer is going to receive the dog. The groomer will (or should) give a thorough bath and brush-out and so on, which will get rid of any dead fleas. Once he gets home, wait three days or so and then check for any live fleas. If you find even one, re-Frontline him.
It sounds like he's a coated breed, if he needs grooming and a cut. One of the best things you can do for yourself is to comb him OFTEN--even a dog with a short "smoothie" cut will mat behind his elbows and so on. Frequent combing keeps his skin clean and will let you know instantly if he's carrying any hitch-hikers.