Very sorry for your loss.
DW and I just recently went through the same a few months ago. Fortunately, the vet's clinic (vet and staff) made the process go as easy as possible. When we called and said we needed to bring our cat in, we were told just to come in without and appointment and they would take care of us. Prior to the procedure, they did go through all the options (did we want to be in the room, did we want burial or cremation, what type of urn, etc) and payment. This way, when the procedure was done, we would be able to leave at our leisure. We were taken to a separate room, were allowed to spend the needed time with our pet, and when we were ready, the vet came in and administered the drug. We were then allowed allowed to stay until we were ready to leave and exit through a separate door. All in all, they made a very difficult time as easy as it could be.