The V5 booklet contains all of the information on the vehicle and it’s registered keepers details.
There’s also a section for new owners. You fill out your details in the booklet, you get to keep a little slip from it as proof, a sort of receipt. Then the old owner sends off the paperwork and you should receive a new V5 with your details in the post from the DVLA.
(Having never bought a car myself either but have bought 2 motorbikes)
The V5C keeper change process can be done online if the previous V5C was issued in the last few years. You’ll still get a new one in the post, but don’t need to post anything.
The V5 booklet contains all of the information on the vehicle and it’s registered keepers details.
There’s also a section for new owners. You fill out your details in the booklet, you get to keep a little slip from it as proof, a sort of receipt. Then the old owner sends off the paperwork and you should receive a new V5 with your details in the post from the DVLA.
(Having never bought a car myself either but have bought 2 motorbikes)