As of version 1.2, Parity works with the Ethereum Foundation Wallet ("Mist").
To use Parity with Mist, you need to make sure Parity is running in Geth-IPC-compatibility mode; to do this just run with the --geth option. For example:
parity --geth
Once it's happily churning away on the network, just run the Ethereum Wallet as you would otherwise and it'll magically use your Parity installation.
If you're running the wallet and seeing only a blank white/black window, your GPU is probably on the blacklist. One workaround is to run Mist with no blacklist:
./Ethereum-Wallet --ignore-gpu-blacklist