When I started hosting I'd ask people (in person, or in a "thanks for staying" note after check-out) if they'd mind leaving me a review "I'm new - it would really help me out..." That did seem to help a bit.
I also have a thing in my guidebook, after the checkout instructions:
Hosts want to know that you’ll be a good guest who will take care of their home.
Guests want to know that I’ll honor their reservation and provide the experience I’ve described in my listing.
After you leave, you will receive a notification to review your stay. Please take a few minutes to provide your honest feedback. This is the best way to let me know how I’m doing as a host, and what is (and isn’t) working for you. It also serves as an endorsement (or warning!) to others looking at my listing.
I’ll be asked to rate you on cleanliness, communication, and your adherence to house rules, which builds your reputation as a trustworthy guest among Airbnb hosts.
Both of our reviews will go public once they’re entered (or mine will show on your profile after 2 weeks if you don’t review me).
Airbnb hounds them with e-mails, too. They get the first when the review period opens (usually the day after check-out), then another when you leave a review. (I like doing my guest review the day after the review opens, then they have 2 days of e-mail reminders!) I think they get a few more when nearing the end of the two-week window.
There will always be some folks who don't leave one - I don't think it's worth sending them additional messages. Some of them seem like guests who weren't extremely satisfied, so I don't want to nag someone into leaving me a 4. 😉