I went to https://www.archlinux.org/download/ then I clicked on a mirror site and a site popped up, but this just seems to be a filesystem. How do I download from here?
Find some mirror geographically near to you. Let's pretend you are French, so it could be https://mirror.thekinrar.fr/archlinux/iso/2018.05.01/
You'll find remote files such as archlinux-2018.05.01-x86_64.iso
You could download the checksum files, like
md5sums.txt to be able to check that your downloaded image was not corrupted during the download.
Then burn that ISO image into a CDROM or an USB key (how to do that might depend upon your current operating system, perhaps you might use Nero on Windows, which I don't know).