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Homebrew is a package management system for Mac. It is under active development and has strict policies to protect the user from damage via software. They also seek to protect users from themselves by avoiding sudo commands as much as possible. It is recommended that you do NOT install homebrew alongside other package managers such as macports/fink.
The following install was successful on OS X 10.8 (Mountain Lion) and OS X 10.10 (Yosemite) and 10.11 (El Capitan). If for any reason this doesn't work for you, I recommend refreshing your terminal (1st) and restarting your computer (2nd) since many of the packages downloaded might require sourcing. If neither solve your specific problem, please send an e-mail to a member of the lab and we'll try to address it as soon as possible. Also, it may be necessary to turn off SIP (System Integrity Protection) before proceeding when installing on El Capitan. To do this, reboot your machine while holding [CMD]+[R], open a terminal from the utilities menu at the top of the screen, type "csrutil disable", hit enter, type reboot, and hit enter to restart with SIP disabled.
Additionally, a known problem of using pure homebrew is that Qt windows seem to possess abnormally large buttons. A way around this is to install Qt/PyQt from source.