You need to understand that the client/server architecture you might be familiar with in your current application won't do. You need to come up with a multi-layered architecture to support applications on mobile devices. There is no simple answer like install an app on your mobile device on which you can build your app. You will need to spend some time to think about which software products and/or frame work you want to use. Do you want to build a native app for Android or do you plan to support iOS in the future too? Basically, do you build a ntaive app for each plattform you want to support or do you want to have a plattform independent app based on HTML 5 and JavaScript?
No matter what it will be the best way to integrate with the backend is REST and using JSON as transport. You can build your REST backend service with OpenEdge or a Java-based (*nix server plattform) or even .NET (Windows based server plattform). If you either use a Java based or .NET based server backend you need to integrate with OpenEdge using the OpenEdge AppServer. For that reason I would build the backend completely on the OpenEdge plattform.
Most OpenEdge developers I know do not (yet) have the necessary expertise. You will have to learn JavaScript and some JavaScript-based frameworks to build the mobile app. Although Progress does provide a development environment - it might not be the best choice depending on your needs.
Heavy Regards, RealHeavyDude.