It has been a while since I played with Archlinux. Meanwhile AUR has transitioned and now uses version controlled PKGBUILDs. So here is how to go about it.
Let us take the example of the package cower.
If you visit that page you will find a “Download snapshot” link under the Package Actions box to the right of the page near the top of the page. Just click on it and you will download a compressed tarball; cower.tar.gz in this case. Uncompress that to find the actual PKGBUILD in it. I also noticed a hidden file called .SRCINFO in the same folder. Now you can simply issue the command “makepkg -irs” in the same directory and you are all set.
The other way is to git clone the repo. The repo link is right at the top of the page under Git Clone URL. If you clone the repo you will find the PKGBUILD and .SRCINFO and .git directory in there. Again use “makepkg -irs” to install the package.