Instead of navigating through the commits, you can also hit the y key (Github Help, Keyboard Shortcuts) to get the "permalink" for the current revision / commit.
This will change the URL from https://github.com/<user>/<repository>
(master / HEAD) to https://github.com/<user>/<repository>/tree/<commit id>
.
In order to download the specific commit, you'll need to reload the page from that URL, so the Clone or Download
button will point to the "snapshot" https://github.com/<user>/<repository>/archive/<commit id>.zip
instead of the latest https://github.com/<user>/<repository>/archive/master.zip
.