I'm assuming you're referring to ranking when someone searches on Yelp as opposed to getting your Yelp profile to rank in the SERPs.
There's not a whole lot of literature/research out their on this topic, but just from experiencing working with clients to claim/complete their Yelp listings, I feel I can speak to it to a certain extent...
One of the more obvious things is having a listing that has content on it. It's not in Yelp's best interest for people to do a search for restaurants only to find a list of restaurants with their names, addresses & phone numbers. So first thing would be claiming your profile and completing the full profile. I don't want to suggest that if you don't have a 'completely full' profile, that's going to hurt your chances, but it can't hurt. Obviously with Yelp, reviews are huge. So you want to encourage real people/real customers to write reviews for you online. However, you've gotta be mindful of the fact that Yelp does a very good job of filtering reviews. So if you tell a customer to write a review on Yelp, and they go sign up for an account, write a review right away, and then never come back to Yelp - that review's gonna disappear.
If Yelp sees a steady flow of reviews, particularly coming from active members of their community, that's most definitely going to help.
The reviews for Yelp are much more crucial than they are for Google. Yelp will sooner show the user businesses with reviews that aren't geographically relevant, than they will show geographically relevant businesses with no reviews & no info on their profiles.
One specific tool that can be useful in terms of driving users to your Yelp profile to write reviews is the Bright Local Review Biz badge.