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