Go to the local registration centre. On the way to Prakonchai past the Imobile stadium. They will issue one.
The car must be fully paid for and not on credit. Not sure of all documents but car reg, house book and ID of registered owner is a must.
Laos is easier to get into but be sure to up your insurance cover. You do need to buy Laos insurance at the checkpoint into Laos but it does not offer much cover.
Getting into Cambodia, so I have been told, is much more difficult