Just be an active user. There is no clear definition, whether it's volume of reviews or rate of writing reviews.
The problem is that you have to manually re-apply every year and your Elite membership can be revoked due to inactivity.
I was elite for several years, but stopped caring because Yelp seemed to stopped innovating. I wrote all these well thought out reviews, but my Elite status didn't really mean anything. I was still on the same level as your stereotypical shitty Yelp review that marks a steak house for not having a vegan option. Why can't Elite users down vote bad reviews by non-Elite users. Nor did my Elitenes ensure that I got personalized search results based on my review profile. Yelp should be doing what Netflix does and recommend good new places. Yelp still does not support private ratings, which I think really hurts the quality of their aggregate score. There is also only one level of Elite, but I think it should be tiered so higher Elites can become mods. I follow a lot of people on Yelp and this is also another completely missed opportunity for them.
And then there's the app, which basically hasn't changed except to push a new product initiative.
It's all just fucking basic, and I just don't really know what Yelp is doing with all its engineers all these years.