How do you install this if one side of the door is rubber flooring and the other side is carpet? Does the rubber flooring go in the groove? How does the carpet stay on the other side?

When using our 1/2" Rubber Floor Ramps going down to carpet, you would put the rubber under the ramp, and the ramp tapered part would go over the carpet. If your rubber flooring and carpet are pretty much the same height, we recommend going with a T-Square trim. You can find proper trims on our Trims and Molding list page.