Setting your price really low is a good way to get requests; even if that means working for $10-15/day until you get reviews. Most pet owners are likely to book with you again after an initial good experience. Don't get discouraged if it takes a while to get requests.
(Make sure you finish your profile to make sure you appear in their search) add a few pictures of yourself, preferably ones that show that you are great with animals. Also, add pictures of your home to show that their pet will be comfortable during their stay.
Doing as many of the medal rover offers helps too since it makes you look good compared to other sitters.
Once you get a request always make sure to let the customer know that you appreciate their interest in having you be their dog sitter! Show interest in their pets likes and dislikes; discuss price only if they seem concerned, insist in a met up to make sure they feel comfortable with you.
Keep your calendar updated to avoid giving a bad impression; since sometimes customers may not contact you again after their initial request was denied.