Hi there, just like other mentioned, ASO is really a good start for app promotion, here are some details on how to conduct app store optimization:
· Keywords Research - when you choose keywords, you should take relevance, competition, and traffic into consideration.
· Add Important Keyword in App Title - the App Title has more weight in the algorithm, which can improve your app ranking by 10.3%.
· In-App Purchases - In iOS App Store, the names of in-app purchases (IAP) are indexed in the app store search.
· Buy Keyword Search Installs - Buying keyword search installs, which can improve your app ranking in hours, highly recommend.
· Get 4/5-Star Ratings and reviews - Ratings and reviews also play important parts in the rank algorithm, helping you show up for relevant key terms.(Reviewapp4u - https://www.reviewapp4u.com/?from=cr-chris provides this kind of service)
· Reduce App Size
· App Updates

Cooperating with influencers is also a good way to promote app, because most people are easily influenced by the words of the influencers. These people may include influential bloggers, newspaper journalists, professional tech writers in a social network like Facebook or Twitter.

Consider Alterative App Stores - Data shows that, if an app is submitted to other relatively less popular stores, it will increase the expected downloads 200% more compared to Google Play.Besides Google Play & App Store; there are various other app stores on the online market where you can upload your app, such as Amazon Appstore, GetJar, SlideMe and ,AppBrain.

Hope the 4 methods are useful to you.