Download the source or use git (check out a tag, though), and then run:
Util/preconfig
./configure --prefix=$HOME/.local
make
make install.bin
make install.fns
make install.modules
(install.docs and runhelp does not work for me)
Then you can add the following to your bashrc to default to zsh:
# -f tests if file exists, therefore only start zsh if executable is there.
if [ -f "$HOME/.local/bin/zsh" ]; then
export SHELL=$HOME/.local/bin/zsh
$HOME/.local/bin/zsh
# Exit from bash immediately when I quit zsh.
if [ $? -eq 0 ]; then
exit
fi
fi