Emma -
Most of the good tips have already been given, but I'll try to help.
PROFILE: Definitely pay attention to your profile and highlight what sets you apart from others in your area. Do you work from home and have a lot of time? Do you have extensive training or experience? Do you love to hike or take your dogs to the beach?
PICTURES: Put high quality pictures of you, your home, your pets, and your neighborhood on your profile. I also include pictures from past stays and from hikes with my dogs, from the Humane Society events we've been to, etc. Make people think "my dog would LOVE to do that!" and they'll want to book with you.
REVIEWS: Have friends/family write testimonials for your profile. If possible, have people you know with dogs book stays with you through Rover. You can always discount your price for them as needed, and then they can write about the fun stuff you did with their dog during their stay.
PRICE: Start low. Look at the average for your area, then beat it. Once you have a few 5 star reviews you can move it up.
BADGES: There are a variety of badges available to put on your account, showing your skills, experience and donations. You can have a Rover run a background check so that clients know you're legit; you can link your other social media accounts and get your Trust Cloud certification. If you have first aid or vet tech certifications, you can have badges showing that as well. There are badges showing you volunteer with or donate to local rescues, and there are badges for those who choose to donate a portion of their earnings to animal welfare. These will help with your search ranking and show clients that you're serious about their animals.
SPREAD THE WORD: Tell friends, family members, coworkers, etc about your new business and have them recommend you. Post a link to your profile on your social media accounts or craigslist (if it's allowed in your area... anything with Rover links is disabled here). See if you can post fliers at local pet shops. The more you advertise, the better.
Finally, don't be discouraged if it takes a while for your first requests. It can be slow going at first while you build a client base. Good luck!
Honestly, I've pretty much given up on Rover. I joined Rover and Wag! the same week. I have 77 completed walks on Wag! with 23 different dogs. I have only had three requests on Rover: one for dogboarding; another in which an owner contacted too many people; and a third had schedule conflicts.