As Spiky says, you’ll need the green V5C/2 green slip and possibly need to complete a V62 Registration application form (but not sure if this has changed since all the DVLA Local Office closed this year and the PO/DVLA Swansea now doing everything) and a V10 Licence application form, along with insurance and MOT.
As you are the new owner/registered keeper I don’t think you can do this on-line.
For God’s sake, before a few things before handing over your money….
If the deal is too good to be true…it probably is!
Check the V5C for the VIN (Vehicle Identification No. 17 digits long) and then check this against the VIN plate (or sticker depending on vehicle make/model) and the ‘stamped in’ VIN located on the vehicle.
Most vehicle have different fonts and possibly security markings before and after the no.
Make sure you get both keys and that the V5C has the appropriate watermarks.
The amount of cloned vehicles I have come across and the unwitting buyers over the years losing all there money has been outstanding and in some cases really upsetting (an old couple spending what little savings they had to only find the car impounded and taken off them was the worse).