I just got a new laptop and am trying to get Linux Mint all set up on it, but when I try to run the Nvidia gpu driver installer, it says it can't run while an X server is running. I tried pressing Ctrl-Alt-F2, but running it from the command line I got the same error. How do I run a program without X running?

Ctrl-Alt-Fx will not stop X server, just switch to another tty. You need to boot into single user or command line mode (when GUI is not started at all).

What is a tty and how do I switch to one?

Read carefully what pan64 said. You switched to another TTY by pressing Ctrl-Alt-F2, but this didn't help because it didn't stop the running X server. Try to reboot into rescue target:

Oooohh, I misunderstood that post. I thought they were telling me I needed to switch to another tty.

Ok, I did manage to quit X and run the installer, but after rebooting, my panels had disappeared, there were no title bars on windows, I couldn't move windows even with Alt, and couldn't close them with Alt+F4. Basically the computer was completely unusable. I reinstalled the OS and tried again, in case something else I did combined with the driver had caused it, but was met with the same result. I've now reinstalled again and have everything working except for the GPU and wireless card (though I'm dealing with that in a different thread).

Turns out all I needed to do was install Mint 20!

If you had the same problem, a blank screen with a flashing cursor, how did you manage to install anything? Did you manage to switch to another virtual terminal and get a login screen on the CLI?

No, I backed up my files, wiped the partition, and reinstalled the later version of the OS, Mint 20.