Interacting with X applications programmatically

I have an application which is built using GTK+. The application has a very simple interface. When started, the same window always opens, with a few input controls. We want to write a script to fill in text in a couple fields, check a check box, then click a button. Pretty simple, and would be easy to do if a command-line version of the app were available (but it isn't). What's the best way to approach interacting with an X application programmatically?