Hopefully changing my car which has a private plate. Looked on the gov website and just confusing myself. I want to transfer my number to the car I am about to buy. If you can explain in simple steps I would be grateful. It appears to be some many different forms.

Download the form, tell the dealer your buying the new car from you wish to transfer the number to it & they should do the rest, oh & charge you £80.
Edit, make sure you don’t transfer ownership of the car that currently has the number on or as soon as you do you lose legal right to it, so if your PX’ing it then get the dealer to give you something in writing that the number belongs to you & is not sold with the car.