Getting the WG to agree is the easy part. Most advertise it on their likes and will charge an additional fee for it.
If you’re just looking to film a bit of head with your mobile then be warned that the footage will unlikely come out great and it actually detracts from enjoying the experience you’re paying for.
I bought a couple of Go-Pros and tripods for around £100 each. I wouldn’t call myself a serial filmer, but there are a couple of WGs who I really enjoy and getting footage is a nice momento.
My advice would be to make sure it’s a WG you’ve already seen before, so you know what to expect. Think about what you’re going to do in the punt, so you have a rough idea of where to position the cam(s) and always aim for as much light as possible as it makes so much difference to the quality of the footage. I try to forget the cameras are there then as, like others have said; first and foremost, you want to enjoy the punt. A ‘real’ punt will always look better anyway IMO.
My filming is for personal use only, so whilst you can never guarantee it falling into the wrong hands, I do take a few small steps to minimise this such as editing it asap so my face is blurred and never film incalls.
I won’t give the WG a copy even after I’ve blurred my face, but I have let them have selected stills and small clips which I’m happy wont incriminate me in any way. The camera’s are battery powered, so it’s easy enough to pick them up and film the evidence of a good cumshot after the main event for example.
All in, it’s a lot of fun, but needs a bit of planning and thinking beforehand if you want to get the most out of it.