Create Youtube video - rank it
Create a website for your app - link it to the google play store, do seo for the website.
Rank the app in the Google Play Store
Put app on other stores like AndroidPit, Slideme, Samsung App Store
Article marketing - link to your website and app
Socially - Get tweets, google plus ones for app - use social exchange website, build social profiles and promote it.
Press Releases - there are a few free ones, get a press release written at fiverr
Answer websites - yahoo answers
Do some email marketing
Search for facebook groups / fan pages targeted to your app market and post
Reviews on the various store are also very important as well as good store descriptions + screen shots
Just a few ideas I came up with for promoting my app and from researching.
Good luck!