Chris has developed and executed leading-edge Internet marketing and communications campaigns for Fortune 500 companies, major trade organizations and a variety of businesses and individuals for over a decade. Currently VP of Internet Marketing for Decantery and the Bonfyre App.
You need to consider good, old fashion SEO. Do some basic keyword research to understand how people might be searching for your app - or what it offers - and adjust or develop web content targeted for that search. If you're able to get rankings for these searches, you'll begin to see the increases and I would even recommend setting up a direct link to the store with analytics tracking to see how many leads that you're sending.
Also, it's not free, but advertising is something you should also consider. Apple launched a simple platform - http://advertising.apple.com/tools/iad-workbench/ - a few months back and there are several other app networks that you can use.
Best,
Clark