I didn't make the wheels myself, I ordered them and I don't know from what material the turner used. What I know is that this plastic is quite common in turnery. For fixing sandpaper on those wheels, I used the double sided tape.
Overall, this is very simple device. It's main components are:
1. the drill - I bought it for € 12 from building store. It is important that it has a variable speed, the rotation revers and the trigger/power switch lock;
2. the shaft support - is made from wood and it has two ball-bearings within it. The ball-bearings are attached to wood with using the construction silicone (neutral one). The shaft support is really important and without it the device is not operating properly;
3. the shaft - it is needed that the shaft is straight and long enough. You can make it from some suitable bolt for example.
4. the wooden base for drill - it's purpose is only to keep the drill firmly in place, it's design is not significant at all.