Clone this repository in oh-my-zsh's plugins directory:
git clone https://github.com/zsh-users/zsh-syntax-highlighting.git ${ZSH_CUSTOM:-~/.oh-my-zsh/custom}/plugins/zsh-syntax-highlighting
Activate the plugin in ~/.zshrc:
plugins=( [plugins...] zsh-syntax-highlighting)
reload zsh
source ~/.zshrc