I have started to believe that most of the new apps which are suddenly rising and showing 10k,50k+ downloads are using android app promotion paid acquisition with CPI (cost-per-install) or CPC. Its hard to say but you should assume a CPI of $.5 per download, more if you specifically target the US/UK market. You can do such ads with Adwords, Facebook, Twitter, GoWide, AppNext etc etc.
User acquisition is just half the story, user retention is the key to success now. How many people actually register after downloading your app, and keep it for a week or more and continue using it. Here you might use Analytics services to figure this out. Google Analytics, AppsFlyer, etc. provide the same.In order to increase retention and usability of your app, you need to tweak your app a little. Use the push notification to remind users if he's not using the app for sometime like 2 days or more. Put a little social inside your app as well to ask users to share it on their social media, or give rating on the Play stores.
1. Own a website and start doing SEO.
2. Have a blog on the website, and update it regularly with fresh content.
3. Create a video of the app and share on Youtube.
4. Create social media accounts on all popular sites like G+, Twitter, Facebook, Pinterest, etc.
5. Put regular contents on the social sites and follow and comments on similar pages, groups.
6. Submit your app for reviews on the app review sites.
7. Submit your app to alternate stores like GetJar, SlideMe, Amazon, etc.
8. Do regular updates for your app and ask users for feedback and/or rating.
9. Do a press release. Outreach the media on your own as well and pitch your app.
10. Make sure to have your presence on LinkedIn, AngelList, CrunchBase, etc.
11. Ask your contacts, friends and family to download your app and give honest feedback.