You need to have a marketing plan..

Define your market segment and see how to reach them.

SEO / SMM / your blog interaction , ads in newspapers or on the streets, or newsletters ... etc. All depends on the target segment..

If you want to share more details about your project, I can help with specific marketing plan.

Good Luck..

Just to add to the great answers already provided, finding influencers (generally, bloggers) to review and recommend the app will go the furthest to gain momentum.

The answer is: it depends. Just like a basketball strategy depends on your strengths and weaknesses, so does your marketing plan.

Do you have a big budget? Go big on retargeting, SEM, and social ads. Hire a PR firm, preferably one that has tangible experience launching apps similar to yours. They will already have the contacts they need to do it right.

Do you have time? Find online influencers who would be reputable reviewers of your product. Build relationships with them. Ask them to review your product, and write content that they would feel happy to promote. Build "a community". Go to events and speak.

If you do not have time or money, you can pray. There really is no magic bullet here. Even Facebook put boots on the ground at campuses in the early days.

Creating a solid marketing plan given what resources you have is your first start. Using a tool like Trello or ProjectPlace to break down your strategy into actionable items that you periodically assess is a good way to make sure what you say actually gets done.

App store optimization is one of the best ways to promote app.it’s the process to optimize apps to rank higher in the app store’ search results. The higher the app ranks in the app stores’ search results, the more visibility for app potential users. Also, the more traffic to your app will be led. Data shows that over 65% of downloads come directly from a search in app stores, so it’s one of the most effective ways to promote apps. These points will help you with your app store optimization:
1.Keyword research - Keyword research is your first task in App Store Optimization and maybe the most important one. When you choose keywords, you also take relevance, competition and traffic into consideration.
2.App Name - Your app name should be memorable, catchy and informative. Be sure to add the most important keywords in app name, which can increase your app ranking by 10.3%.
3.App description - Be sure to highlight your app advantages and features in the first 3 lines too.
Category - Choose the right category should based on what is most relevant and the level of competition and generated revenue.
4.Place the keywords in the name of in-app purchase items, which can also increase the app ranking.
5.Make your app icon, screenshots and video attractive, which can increase the download rates directly. More downloads, higher app ranking.

App store optimization is not a week- or even month-long project. You should be patient. You also should monitor keywords ranking regularly, then you can get the best keywords for your app.

Besides these methods, you can also get app installs to assist ASO, which can boost app ranking in hours, ASOTOP1(http://www.asotop1.com/?from=cr-chris) provide app installs, which supports multiple countries and install types for you to choose from, get your app targeted precisely, highly recommend.

Hope these methods are useful to you.