Prepare your expectations accordingly. Have you been collecting emails from a landing page while you were developing? Do you have organic search traffic coming to your site? Do people know about your app? Have you validated the market for your application?
If you answered no to those questions, expect zero people to know or care about your app. Launching and running a successful web app is 10% development and 90% marketing.
I'm telling not trying to discourage you, the opposite actually. Just because no one signs up when you launch doesn't mean your app sucks. It means no one knows about it. Start marketing, start blogging, start SEO, start guest-posting, start doing everything you can to get the word out.
As an aside, you should probably have a way to monetize the app in mind and put it in place before launching. Very few apps can get away with ads or freemium effectively, especially if it is a small micropreneurial endeavor.
Edit: Looks like you have an email list. That will help you convert well on the first few days and give you a morale boost. Don't worry about the rest, tackle it as it comes. You'll never be ready enough, so just go for it when you have a working product :)