We are members, so we have not rented from another member. I can explain how it works for members though so you can tell the member what to expect.
You need to figure out what you need - do you need a fully wheelchair accessible room with a roll in shower, or just a room with grab bars in the bathroom. There is more information in the disABILITIES FAQs thread about the different types of room (including some pictures). There are also rooms that have features for people with hearing disabilities. A link to the disABILITIES FAQs thread is in my signature.
Once you know what you need to reserve, it's important to make sure that the person you are renting points from understands what you need. The member needs to make the actual reservation.
For the rooms with roll in showers or grab bars, the CM taking the reservation will contact Special Needs reservation to make sure that there is actually a room with those features available for the time period you want. If there is, that room will be blocked for your reservation. They won't tell you which room it is until you check in, but it should be blocked off for you.
The confirmation sheet for your reservation should say something like "Fully accessible villa confirmed" (or whatever the needs were), although our last DVC reservation did not.