Simulate user interaction

Can user input be simulated? And how can I figure it out?

I need to automate user interaction with a Windows application. The problem is that this app does not provide an API for one special function that I need to call. But this function is available in the application window using standard mouse input.

I am not tied to any programming language. I only need to write an application that does the exact same thing that I do using my computer mouse input.