First (if you don't already have it) get multirust:
Linux:
curl -sf https://raw.githubusercontent.com/brson/multirust/master/quick-install.sh | sudo sh -s -- --yes
OSX with Homebrew:
brew update && brew install multirust
Then, download and build Parity:
# download Parity code
git clone https://github.com/ethcore/parity
cd parity
# parity should be built with rust beta
multirust override beta
# build in release mode
cargo build --release
