it is gonna be hard. The best way to get free downloads is to be in top of the app store/google play. You can chech how many donwloads you need to get to reach the top and make it as youк target. Check here how many installs you need, it depends on the app store and your app category. Try to find here https://www.appannie.com/insights/. App Annie has acquired Distimo, the company that made lots of reports on such kind of data.
You can try tо get free installs via:
- posts on relevant forums, fb app communities, reddit relevant communities - the goal is to ask for a feedback of those communities, ask them to try and tell what is good and what is not. Don`t forget to put a link to install your app.
- pitch relevant bloggers, if the app is interesting they can review it for free
- the hardest is to invent something viral, like cool tweet to share inside the app. For example, {Name of your app} just calculated I spent X hours wathing TX series today. Calcalute your time {link}.