This is something I have been doing since my kids have been in cribs to save myself time, stress and sleep!
I bought two sets of sheets and two sets of waterproof mattress pads. Make the bed first using the first mattress pad cover (goes on top of mattress), then following with the fitted sheet, and regular sheet. On top of that, put the next waterproof mattress pad, 2nd fitted sheet, and 2nd regular sheet.
When your child gets sick in the middle of the night or wets the bed, you can do this fix in the dark so that everyone can get right back to bed. And as they get older they will learn to do it themselves!!!
The reason I posted this today is because this happened just last night. Brody wet the bed and he knew to pull off the top layers, change his clothes and get a new big blanket out of a drawer in his room. I didn't even know all this happened until he got up this morning and told me.
So to add to this, what I have done was put a spare set of jammies, undies and a big comforter in the bottom drawer of his dresser. He knows it is in there, so if he has an accident, he can change the sheets himself, change himself and get right back to bed, barely interrupting his sleep and not interrupting mine at all :) Since he is five now, I think this is a fine thing for him to be doing on his own. Even though it was an accident, it causes him to be responsible for it and hopefully he will have less accidents.
Here is a picture: The blue set of sheets are the first set which are over the 1st mattress pad cover. The white is the 2nd mattress cover, and the orange is the 2nd set of sheets.