Out of the box, Homebrew does a default installation on Sphinx:
$ brew install sphinx
However, if you're using MySQL, the thinking-sphinx gem won't work because it needs to use MySQL libraries.
If you managed to screw up the first time, uninstall sphinx first:
$ brew remove sphinx
and do an interactive reinstallation:
$ brew install --interactive sphinx
This will take you to the installation folder, so you can do additional commands yourself. Add MySQL dependencies by doing:
$ ./configure --with-mysql
$ make
$ make install
When I try --interactive method, I end up with a message saying "Error: Empty installation". In this case I used --mysql=/user/local in stead of /user/local/bin, to avoid an error message.