I am a complete beginner and wish to photograph my cats on plain white backgrounds with the cat appearing very crisp and detailed. Can anyone tell me how to achieve this without buying lots of expensive equipment please?
A beginner level DSLR with a kit lens would be enough for this use case. Taking into consideration you're a complete beginner, you probably can just use auto-mode for this task. If you are wanting to get into photography seriously or just really need a super crisp image I would suggest buying a prime lens (maybe a 50mm).
It doesn't require buying a lot of expensive gear, but it does require buying gear. And you don't need a dSLR, you need a lighting setup. And going into studio-style lighting setups requires a bit of experience and knowledge. This might be a look you can achieve without lighting, but it's unlikely.
The white background and crisp clean look are generally done by lighting the background and the subject separately. So you need at least two lights, but probably three. You need some way to trigger them. You need the backdrop. You need enough physical separation and control of the light spill so that they're completely separate areas of light. The background is essentially overexposed enough to be white relative to the subject in-camera.
So you'll probably need to master off-camera flash, which in turn is easier to do if you're mastered M mode on your camera, which in turn is easier if your camera has an M mode and a flash hotshoe.