Out of the box Mac OS X version 10.8.x (Lion) comes with zsh version 4.3.11 (i386-apple-darwin12.0). However zsh is currently at version 5.0.2 (x86_64-apple-darwin12.2.1). Here's how to use the newer version.

Install zsh using Homebrew.

$ brew install zsh

Edit /etc/shells to add a new entry for the Homebrew zsh.

$ brew install zsh
$ sudo vim /etc/shells

The resulting /etc/shells file should look like this:

$ cat /etc/shells
/bin/bash
/bin/csh
/bin/sh
/bin/tcsh
/bin/zsh
/usr/local/bin/zsh

The /usr/local/bin/zsh location is the symlink Homebrew creates when installing zsh.

To actually change the shell assigned to your user account run

$ chsh -s /usr/local/bin/zsh

Now you have the most recent zsh as your shell.