How you go about publishing your web app depends on what platform you created it in. Is it PHP, a Python or Ruby based framework, .NET, Java, node.js, or something else completely?
I'm actually looking for some suggestions on how to market and launch the app. For example, I'd like to get some people testing it and I'm also wondering about how to get some buzz around it. Finally, at the moment I'm a full time employee and I don't have unlimited money/time to fund the project.