I followed the instructions from https://github.com/TryGhost/Ghost#developer-install-from-git with a few tweaks. You need to run the
npm install commands using sudo (they will fail and then tell you to rerun as root). I also downloaded and installed Node.js v0.10.40 from install package. Node.js v0.10.40 has several security fixes and is probably a better choice than v0.10.36 I saw recommended somewhere.
Surprisingly easy to get it all running when I figured out that
npm install needs root permissions and
gruntdoes not after a tip from @acburdine in #ghost on Ghost Slack.
Edit 2015-07-19: It should be possible to run
npm install without
sudo, according to @fabian over at Ghost Slack. I'll see if I can reproduce my troubles from yesterday and figure out what was wrong.