Fear of the unknown is a real thing here.
With my first dog (who lived to be 17.5) I made appointments, cancelled them, cried, was generally a wreck. I didn't know what to do, how to do it, what to expect (well, I worked at a vet clinic, so I knew the physical part, just not the personal emotional part of euthanasia), etc. I was surprised at how relieved I felt afterward. He was really a high-maintenance senior dog (for years) and had a difficult temperament, especially in old age.
There were some lessons learned.
I wish I had done it at home. I didn't particularly like the attention at the clinic, even though I have known my vet for 20 years. I didn't like being hugged by the staff or crying in front of strangers. It was also very clinical. I also wish I'd done it at home because Sam was confused about the dog's absence for a couple weeks, which felt helpless and kinda dragged things out. At the clinic, you can take the dog home or you have other options, like group cremation (don't get ashes back) or private cremation (you get ashes back -- more expensive). I think I paid about $100. I opted to not take the ashes. He had a good long life and it would not have made me feel better to put his ashes in a place he loves. But that's just me and my belief system. I have no regrets not keeping his ashes. I kept his collar, photos, memories...
With my second dog (who lived to be 16.5), I did it at home and afterward, I let my two dogs come and see/sniff him. This dog was difficult as he was all there mentally, but physically, his body was shot. Afterward, the vet takes the dog (if you don't want to keep the body) and the options are the same as above. It cost me about $250 or so doing it this way. This time, I called when I was certain and never cancelled. I felt more confident in my decision this time.
As far as having someone with you, I chose not to. I don't really have anyone close in my life who would understand my relationship with my dogs and it's a personal thing that a lot of people I know, including family, do not understand. After my last dog died, I didn't tell anyone until after because I wanted some time alone and didn't want the texts and emails and calls right away. This is a personal decision that only you can make.
I don't mourn my dogs before they go. I go day-to-day and am happy for the time we have together. I won't think about declining health until it happens, and even then, you have good days and bad and I try not to get sucked into that because it's an emotional rollercoaster! Of course, I have numbers, names, etc. in the event that something happen at home to either of my dogs, regardless of age. A dog can go down at any time (choking, seizure, injury, etc.). We do all the things that people do with their dogs on their last days on a regular basis -- hiking, trips to the beach, ice cream cones from DQ just for fun, a good steak for dinner, swimming in the river, sleeping in the bed, weekend at a cabin in the woods, etc. -- so I don't do the last day stuff, either. I might want to spend the last day together one on one or sit with them awhile or something -- feel like I'm saying my good-byes.
It's always hard though, even when it does get easier.