You haven't specified if you're using Python or Java.
You have to decide how you want to connect. At the simplest level you could just POST the data to Google App Engine. In Java you would write a servlet which handles this. See Java EE tutorial. Alternatively you could write a web service (SOAP, RESTful) on the server which handles the data being sent from your application. Again Google this and there are countless examples.
Assume we're going down the simplest POST route. So in your servlet (running on GAE) you'd have something like this:
public void doPost(HttpServletRequest request,
HttpServletResponse response) throws ServletException, IOException {
String value1 = request.getParameter("value1");
}
And in your android app you'd do something like:
DefaultHttpClient hc=new DefaultHttpClient();
ResponseHandler <String> res=new BasicResponseHandler();
HttpPost postMethod=new HttpPost("http://mywebsite.com/mappedurl");
List<NameValuePair> nameValuePairs = new ArrayList<NameValuePair>();
nameValuePairs.add(new BasicNameValuePair("value1", "Value my user entered"));
postMethod.setEntity(new UrlEncodedFormEntity(nameValuePairs));
String response=hc.execute(postMethod,res);
Of course value1 in the servlet would be set to "Value my user entered".
EDIT: Google have now released their Google Cloud Endpoints - this makes building RESTful services on App Engine and creating clients for Android a lot easier. It does tie you in to App Engine even more though - but certainly worthy of consideration.