This all depends on your budget.

But fundamentally... you have two options:

1) Buy media

Using AdMob or some other ad network provider

2) Generate buzz

These can include things like building a website for your app with some basic SEO running on it and perhaps a small media buy (budget restricted) using adwords

Then, contact app review sites - there are loads of them

Facilitate a JV partnership with other app owners in your niche / vertical.

Would suggest avoiding doing press releases - they just don't work very well.

There is a 3rd option, but sounds like you don't have a budget to work with and that is by working with an app marketing agency (e.g. app promo)

Good luck :)