Do you want to authenticate the login to the Android application using the username and password from your DNN site?
If so, I think that the best way to do this would be to create a webservice in your DNN installation that you can call from the Android application. When you click the login button in the Android application, the result would be to call the webservice to get a yes/no answer for authentication.
You will want to have the latest version of DNN to do this.
There are modules available that simplify the process of creating webservices in DNN. I believe that DNNSharp.com has one. Also, the module from
http://2sxc.org/.