Once you have your profile set up, all you can really do is wait. There are a number of things to bring yourself up in the search rankings without already having sitting jobs, so just be sure you've touched all those bases.
PROFILE: Make sure it's filled out completely, and that you're very clear about what services you provide and what sets you apart from others. Upload high quality pictures of you, your home and yard, your pets, and anything else you want to highlight. I include pictures of places I frequently take my dogs and those I sit for - local parks, hikes, the beach, etc. Now that I've been doing this on Rover nearly a year, I've been able to add in a handful of stay photos to my profile photos to show what past dogs have been treated to, but you can do this with your friends' dogs as easily as client's.
TESTIMONIALS: You won't have reviews yet, but testimonials will help in much the same way. Get your friends and family to write these for you, especially if you've watched pets for them in the past. If you're really ambitious, you can have a friend book a stay with you through Rover (you can adjust the price as low as you want for them once a stay is requested) and once the stay is completed they'll be able to leave you a real review. I don't think this is necessary, but it won't hurt.
BADGES: The more badges you have, the better your search ranking. There are quite a few out there, so look through them to see what applies to you. If you ever donate to your local shelters or volunteer your time, there's a badge for that; if you donate a percentage of your earnings to a charity, there's one for that; you get another for completing a background check; there's yet another for completing a pet first aid course.
Then you just have to wait. For me, with a complete profile, a few badges, and a couple testimonials, I booked my first Rover client in about a month. Like any business, it will take quite a bit of time to build a solid client base. Good luck!