There's not a great way to do it right now.
When GDK was announced, there was reference made to an authentication API, but it is still in development. An early version is used by the Strava Glassware. When it is released, it will use a REST API much like the Mirror API to convey authentication information to your user's Glass. You will then be able to access it using the AccountManager
.
In the mean time, you can work around this issue by sending authentication data to Glass using a QR code, but be ready to switch to the official solution once it is available.