I chose it because it seems to be more actively developed.
As explained on https://github.com/mxcl/homebrew/wiki/installation I installed Homebrew like this:
/usr/bin/ruby -e "$(/usr/bin/curl -fksSL https://raw.github.com/mxcl/homebrew/master/Library/Contributions/install_homebrew.rb)"
I had XCode already installed, but If you don't, you have to install it before following the next steps (in order to have gcc etc. installed).
update 2012-03-24: Nowadays you don't need to have XCode installed anymore. It's enough to have the Command Line Tools package installed which you can download from the Apple developer network (free registration required /Apple Mac Dev Program required for pre-releases of the tools).
What I Brew
brew install wget pwgen nmap mtr bmon
brew install pyqt
Upgrade all Outdated Packages
brew outdated | xargs brew install
update 2012-03-24: the above is not needed anymore. Just use