The AUR is essentially a non-curated repository of scripts named PKGBUILD which perform some actions and build a package pacman can install. The expected way to use it is to download the PKGBUILD file to a folder, read it to ensure it is not malicious and run makepkg which will generate a package you can install with pacman.

That being said most people use a helper which does all of that automatically. My recommendation is to install yay or paru using the process I mentioned above to understand it, and from then on use that program to install new stuff. Both of them are drop-in replacements for pacman so you can use them for all package installation.