This turned out to be much simpler than I thought it would be.
I began by installing unixODBC, though I'm not sure whether or not that ended up being needed:
brew install unixodbc
Then I installed Free TDS:
brew install freetds
Then I installed the tiny_tds gem:
gem install tiny_tds
And that was it. I was able to connect up straightaway as described in the tiny_tds documentation:
For further details see the tiny_tds github page.