Hi Dotname, welcome to Acorn.
As long as you're dealing with trusted/established members who have good domain trader ratings, and/or are long standing members of the forum, it's very simple and safe to deal with them.
I sold a domain on here earlier, I sent him the invoice and the domain transfer, he's not paying me until tomorrow, but I know he's trusted, so I'm happy to send the transfer before I get payment, as is the case with just about everyone on the forum I've dealt with. Some members on here wont even accept the transfer before they have paid.
If it was a new member I was dealing with, and I was buying a domain from them, I would expect to receive the domain transfer before I sent payment, same if I was selling a domain, payment first, although I've had sales with many new members and all has worked out fine, we were all new here at one time.
Most payments on here are through PayPal or BACS, if you sell through the likes of
www.sedo.co.uk -they offer in house escrow service to protect buyer and seller, but there are fees if you sell on Sedo, normal fees are 15% and they're 10% if your domain is listed with a buy it now price.
When transferring .UK domains, that is done via
www.nominet.org.uk - the seller will log in to their Nominet account an initiate the domain transfer, in most instances, it is the buyer who pays the transfer fee of £10 + VAT, unless you have an agreement with the purchaser that you will pay the fee, but if you put in your post that buyer pays the fee, that's all done and dusted and they pay.