Can anyone tell me how to go about getting a set of private plates?

Buy from DVLA (their prices include £80 transfer fee, some companies don't)
DVLA send you certificate
Take to DVLA office (or you can post it) with form filled out and they'll do the rest for you

so do i just go on the dvla website for that?

there are also companies like http://www.regtransfers.co.uk/ - iirc mine cost £189 via them & was painless.
You can pay an awful lot more though depending upon how desirable the no. is seen as being.

[url="http://dvlaregistrations.direct.gov.uk/"]http://dvlaregistrations.direct.gov.uk/[/url]

Thanks what happens if you get a new car? Can you get the old plates put back on then transfer your private plates to the new car?

[quote name='DanGersFord' timestamp='1358257342' post='226973']
Thanks what happens if you get a new car? Can you get the old plates put back on then transfer your private plates to the new car?
[/quote]

Yes and it will cost you £80