If you play with "Capture the Princess" on, I think you should capture her with another unit and carry to your Capital to get Victory Points. When you move a military unit on the tile where the Princess stands, you should see a command icon (near "Rename unit", "Fortify" and others), which, when you click on it, allows you to "tie" the Princess to your unit. The Princess should go everywhere the "captor" goes.
I haven't played this mode for a long time, and I don't know if it works as it was intended.