I pulled all the stuff out from under the sink, got myself a couple of working flashlights, a bucket, and a pair of pliers, and I set to work. I turned off the water to both sides, tested to be sure it was really off, and got ready to unscrew the Hot and Cold water tubes from the current faucet.
It's really hard to both see what you need to unscrew and reach it with the pliers at the same time. It's kind of like Heisenburg's uncertainty principle that way.
I spent a lot of time contorting myself and straining. A lot.
I finally managed to get my pliers onto one of the hex nuts and I could SEE it at the SAME TIME!
But I found out that in order to get the pliers that wide, they became to wide for my hand to hold and turn them.
This made me take a second look at faucet pieces I was trying to unscrew the water tubes from. They looked pretty big. When I checked the still-attached tags on the water tubes, it said they were for 1/2" connections.
I checked the new faucet. Not 1/2". So now we need new tubes.
I gave up, turned the water back on, and put everything back under the sink (bonus: it's organized a lot better now). I guess we'll just call a danged plumber to come do it for us. Or maybe I'll get brave and get my own new hoses, since I am pretty sure I know how to figure out the right ones to get. And new hoses might make the job a LOT easier. I could unscrew them from the water end and pull them up through the sink when I remove the faucet. Then attach the new ones to the faucet before bringing them down to the water shut-offs.
There is probably a reason why that won't work, and I will probably figure it out while I'm trying to do this again next week.