I have carpet in a bedroom that I am thinking of replacing with a hardwood floor, but the bed has big wooden feet and they might scuff the floor. Is there a standard way to protect the floor? Maybe a rubber pad or cup?
The bed has "big wooden feet"-- how big? A large cross section of the ends of the feet decreases the pressure at each point and reduces deformation of the floor. You might be able to use the bed as is with no significant damage to the floor.
You can buy glider pads for furniture and keep them under the legs all the time. Or you could make support pads for the feet of the bed out of 1/2 inch plywood. A square 6" x 6" should be enough, then cut off the corners to make an octagon. Slightly relieve the edges with sand paper so that it doesn't leave edge marks.
Some furniture manufacturers put metal buttons on the bottoms of wooden legs. Does your bed have those? If directly in contact with a softer floor, those will cause deformation and scratching. If your bed has those, and you decide to use the bed without pads, pry the metal buttons off with a screwdriver. But if you use wooden pads you can leave them on, especially if you make a slight depression in the wooden pad for the buttons to fit in.
I would consider either rubber feet (thick rubber designed for furniture, not just a sheet of rubber because it will tear) or sticky felt (one side is sticky, the other is felt). I use rubber on our couch. It doesn't move and protects our wood floor and felt for our furniture we don't sit. If you felt furniture you sit/lay on, it will move around the room.