Nate, good question, and I like how you asked :)
I think the easiest way to install curl is with this page:
I downloaded curl-7.46.0-win64-local.msi from that page and installed it. That's all you should need because it will put curl.exe in a folder and add that folder to your PATH environment variable - so the TRIGGERcmd will be able to find it.
To test it outside of TRIGGERcmd, just open a cmd prompt and type:curl www.google.com