Great question! Since 60% of App Store customers use search to find apps, ASO can help you boost sales.
It's a big topic but I think the basics are to optimize those parts of your profile that are being searched by users - your app name (make it keyword rich if possible), your keywords (use terms that are popular but not overly competitive), and your company name (if you haven't created it yet).
I'd love to do a review of your app and give more ASO tips... let me know if you want to chat.
I will not go into too much details but I want to mention that store optimization is a good place to start but it will not get you too far.
High quantity of downloads and reviews gets your app noticed.
The more downloads and reviews your app gets, the more people will think: "If that guy (girl) liked it so much - let me download it 2". And then the app gets the 'snowball' effect - keeps getting bigger and bigger. But you need to promote the app.
There is so much to be said about this… It's like asking the same for SEO, 10 years ago.
App Store Optimization (ASO) implies leveraging to elements: enhance visibility (high rank in results) and improving conversion (compelling artwork).
Although there are common strategies apps usually implement to achieve this, the tactics will be very different depending on target demographic, competition and nature of the app.
you can find more details (multiple posts) here: http://giacomoballi.com/?s=app+store+optimization