What's an effective way to get my name out?

post only a few flyers in stores where people go who have pets like pet shops or vetrenarian clinics

Well what i would do is just pay a couple dollars to put your name in the news paper and say that you are going to start a dog walking Business! I hope that this helps

You do know, of course, that you'll have to contact your local county/city office to obtain a business license. You'll also need to get a liability policy to cover you incase a dog is injured while in your care. You will also need to be bonded.

I would leave flyers at apt .that allow animals. and maybe some of the larger county parks

Craigslist.com, Backpage.com, flyer's at the vet or even pet stores.

go to the vets offices and see if they will put up a poster for you

go onto the football field naked holding up a sign. everybody will know you after