Simple - well, if you have an Android phone - go to https://accounts.google.com/sesame and it shows a QR code (one of those 2D barcodes). Scan that from the phone and it asks you (on the phone) if you want to allow access. If you say yes then the PC is automatically logged in to GMail.
Works on non-Android phones too, apparently - but they don't have your account info stored on them, so you have to log in on the phone to tell it who you are.
Original post on Dreamwidth - there are comments there.