hi there
dead simple!
purchase the plate from them,(transfer fee is included in the purchase price)
when the paperwork arrives -if near enough you can go to your local dvla office with the paperwork for the vehicle you wish to put it on (mot, tax disc,registration document) & your cherished number form V750,you will have to fill out form V317 normally only available at the reg/office,they will process it ,then normally send it back to you in a few days --i dont think they do it on the spot now,when you receive your documents you will have a form V943 -number plate authorisation certificate,so you can have your plates made up, you should get your tax disc included /to run to the end of original expiry date. you should then return the old tax disc.
within ten days you should get your new registration document back.
If you have a new style mot certificate! this will also be reprinted to the new reg details.
it sounds long winded but i have just transfered mine AGAIN.
dont forget to tell your insurance company when it is all done!
good luck