For Cars (I am assuming Motorbikes).... it goes like this
Find Car in UAE - and buy/get Export Plates Sorted out. This will be more of a pain than you think - because OM and UAE have different weekends.....
Take the vehicle (and temporary Insurance) - plus as many documents that relate to how the vehicle was imported into the UAE as possible that you can get.
Proceed to Hatta Border - UAE Customs will inspect the vehicle and give you some more paperwork.... hopefully you can drive over the border now....
As Soon as you go over the border - stop and Buy Oman Insurance !! The ROP will check (If your bike is on a trailer - it does not need at this point to be insured).
Next is ROP Customs.... they will assess the vehicle - in reality ask you for the UAE bill of sale.... if all those other documents do not prove the GCC Customs duty was paid on this vehicle - then you will be charged 5% on the Bill of Sale amount....
The ROP may not put their brightest on the border - but bringing a Ducati XXX in and only paying 500 AED will not work,,,, they are not that dumb.
Assuming you pass this stage.... You need to go to Sur/Muscat, get Proper Insurance then go to the ROP Vehicle Inspection/Registration - Here you get the forms for registration, they will inspect the vehicle, and issue a license plate.
It sounds terrible - but if you keep calm, smile, and are lucky - it is not a major issue.
Hops this helps