How should I promote my Android app to get more downloads and reviews?

First of all you must be sure that your application is good at what it did and you can really count on it. Clearly you already done it, I suppose. So look at the social medias page and groups platforms. Like, Android groups of that so many people hang in it and share their ideas about their applications. And besides, if you do that, you can take so many feedbacks that you can improve your application. You can find these kind of group on Facebook so much, but don’t get in everyone, look for with the quality ones.

After that you can start opening social media accounts that giving some kind of informations about your application, like where you hide little things or what should user do if he/she wants to get this part easier.

And after, you can give ads to Google, Facebook, Twitter, and some blogs.

Try some paid app campaign, etc.

By the way don’t forget to write a blog about it.