It sounds so easy, and I believe it is, for some...
When I click on the signed hash file, it opens in a new window in my browser and I see no option to download the file, so I copied the content and and made the file myself by naming it "armory_0.92.3_sha256sum.txt.asc".
File > Save Page As in your browser (at least in Firefox). But what you did works fine too.
And then I ran the code you gave me and it said it was a good signature. But when I run this command:
sha256sum armory_0.92.3_osx.tar.gz
it says
-bash: sha256sum: command not found
My mistake, I forgot that sha256sum is only on Linux and not on OSX out-of-the-box. Try picobit or doug_armory's solutions.
They should probably have OSX-specific instructions for verifying the installer on the download page along with the Linux one.