Facebook is the largest social network in the world and if you consider Facebook a nation, it will be the most populated country in the world. So it is a huge pool for you to draw users to your android app.
The fastest way to do Facebook marketing is to run Facebook Ads and I wanna suggest a FREE extension to make your ads more catchy (and even save costs): cool text generator. It will create stylish & funny text to make your ads stand out from the crowd. I have tested it and the CTR of ads increased by 23%.
Another tool to let your fans (if you have fanpage) invite their friends to try your product is this: facebook invite all. Create an event to launch or update of your app and tell your fan to use this tool to invite their friends to the events quickly.
The 2 Chrome extensions are completely free and easy to use, so you can try it:) Hope it helps !