"Write an application that starts with an Activity with
 a Button, opens another Activity with a TextEdit, which then
 returns the edited text to the first Activity for display."

This example from a past class will get you started: 
  http://www.cs.dartmouth.edu/~campbell/cs65/lecture03/lecture03.html
     
Note that to return back data from another activity (rather than just
dismissing it), you need to use startActivityForResult() rather than
startActivity(), and pick up the result in onActivityResult().

Menus are convenient, but not required. You may leave out the
functions onOptionsItemSelected() and onCreateOptionsMenu(), and
instead use a Button to call finish() to dismiss the second Activity.