When I started grooming I put an advert in the local paper for 3 months - that gives people who don't need you at the time to find you later when they do! After that I didn't need to advertise for the next 20 years -the quality of my work was my advertising and bought me in enough dogs to need a waiting list. :)
Grooming here. I have an ad in the village newsletter, I keep it up as people move into the area looking for grooming, and if I just get one new client from it in a year it pays for itself. Otherwise it's mostly word of mouth.