You don't download or install aur itself. It's a repository of packages.

Helper programs like paru make it easier for you to connect to, search, download, build and update packages from the repo.

You can also use other methods, for example 'git' to clone the source for the package and build it yourself, but the helper programs should also help fetch dependencies.

As with everything in arch, the wiki is recommended reading:
https://wiki.archlinux.org/title/AUR_helpers
https://wiki.archlinux.org/title/Arch_User_Repository