Interacting between multiple applications interfaces can be tricky, so it may help to provide more information on specifically what you are trying to do.
Nonetheless, you have a few options if you want to use the clipboard to accomplish this. On Windows, the Windows API provides GetClipboardData and SetClipboardData. To use these functions from Python you would want to take advantage of win32com.
On Linux, you have two main options (that I know of) for interacting with the clipboard. PyGTK provides a gtk.Clipboard object. There is also a command line tool for setting the X "selection," XSel. You could interact with XSel using Python by means of os.popen or subprocess. See this guide for info on using gtk.Clipboard and xsel.
In terms of how you actually use the clipboard. One application might poll the clipboard every so often looking for changes.
If you want to get into real "enterprisey" architecture, you could use a message bus, like RabbitMQ, to communicate between the two applications.