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:
@xander, good progress.
The reason only Calculator and Notepad show up is you're only running a foreground agent. The background agent won't work in your case because you're using the basic 32bit Windows agent. The foreground agent reads foreground commands from commands.json, and the background agent reads the background commands.
Are you able to run the commands from the green Trigger buttons on the website?
Do you get any output in your cmd window when you trigger a command from the website?