To change which group a vehicle is assigned to, from the side menu select My Assets.
Click the blue Profile button under the vehicle you wish to update.
This will take you to the vehicles' information page where you can then add or remove the vehicle from a group.
To add it to a group just click the group box and all the available groups will drop down. Just click on the one you want the vehicle to be assigned to and it will appear in the group box.
To delete a vehicle from a group, click on the X within the group box and it will remove this group from the vehicle.
Make sure you press the blue Save button to save your group changes.