I feel I got pretty lucky with marketing. My best guess is that word-of-mouth has played a big part in the app's growth. People love to show off, and it turns out that Tiny Piano is a fun way to show off something cool to friends.
But specifically, I have two Facebook pages where people can like my app/company and get updates: https://www.facebook.com/squarepoet https://www.facebook.com/tinypiano
If someone likes my app, it'll show up in their profile. So there's a chance that their friend will also find my app.
I also include an "Email a Friend" button in the app. People use that button to share the app with friends.
As an engineer... I don't enjoy marketing. But I know it's super important, and I'll spend much more time on it going forward.