How to Wrap a Twin or Full (Double) Size Mattress
Open the cover.
Slide your twin or full mattress in like this. This is a rather thin mattress. You can see there is more room on the ends to accommodate a thicker mattress. But for the most part, the twin fits in perfectly. At this point you can either cut off the extra plastic, or...
Fold the extra over the mattress like this:
Fold it over again. This is the bottom of the mattress.
To vent your mattress, you will need to cut holes on the part of the plastic marked here. Secure the flap with tape. The "extra" amount will be different for every mattress. This is a thin mattress, so I can't imagine any other mattress having more left over than this. A full size mattress will not have a second fold over, but it should be covered just like this. On this mattress, the ends were not taped at all. The creases for the gussets kept flat and there was little extra to worry about.
Here is the mattress with foam padding, mattress pad, and sheet. If you would like to see how this bed sounded when rolling over in it, check this out.
Queen and king size mattresses are inserted the "right way" and then extra plastic can be wrapped underneath. The closer your mattress is to a 15" king, the less extra you will have to deal with. The end of the wrap on king and queen mattresses should be folded under (can be folded a few times so the open end is tucked inside) and then taped to the bottom of the mattress.
People are often concerned about the vent holes, because they want to keep all the gases inside the mattress. I know this seems counter-productive, but it is not. The gas has to go somewhere. Vent holes allow a slow escape. When we wrapped a memory foam mattress that had lost it's stink, I was surprised at the horrible stench that escaped when we accidentally ripped the cover. It had kept in something I hadn't even realized was still there.