How should I go about making an application with C# and .NET where, say, on one computer a button is pressed that triggers an event on the other?
I saw this:
Recommended way to communicate between processes running on different computers on the same network
I’ve never heard of WCF, is that what I should try?
Yes, I would use WCF, because I know it’s pretty easy to get a simple project running with WCF, and that will give you confidence to build on it. (Having said that, I dont have much experience with any other networking technologies.)
Start with this Getting Started tutorial.
Then if you have more specific questions, ask them.