Hi Hodu,
You just go to the hospital and register at their cashier window, if you want to go to QE just go to the ambulatory care building which is on queen Elizabeth hospital path and their clinic is on the 4th floor. The want to your ID card, and your partner's ID card, and proof of address. Your partner doesn't have to be there. They don't do telephone bookings for the first appointment. I don't think I had to pay that time, I think I only ever paid when I was having a procedure done, like a scan or something, and then it would be a small amount, like $150 each time.
Kwong Wah is actually really close to QE, so I would guess they can't be that different from each other, but QE is bigger and I heard more feedback about it. I don't seem to have come across anyone who has given birth in KW for some reason.