You can try Review Exchange. It will help your App to get the initial popularity, then you should be able to hold the users who use your Application with your unique features and awesome UI.
You can of course buy ads, but if youre looking for a free solution you should promote your app on forums and such. Thats because the posts stay visible for a long period of time so potentially they can be seen by many people
You can do it in 2 ways:
1. Pay advertisers to advertise your app/game in either cross promotion and paid reviews.
2. Put an effort to talk to a lot of people in groups and forums to test your game. This may take some time but it is somehow applicable to those developers who have no budget.