Standard-size quilting cotton works GREAT, however I do love the ease of extra wide back quilting cotton or sateen cotton--it's extra smooth and silky feeling.
The ultimate Tula Pink bed sheet.... All you have to do is make sure to MEASURE accurately --both your bed mattress, and then the fabric you are cutting. I walk you through each step. There are lots of diagrams & photos to help keep things extra clear.
Supplies you will need depends on the size of the mattress you're covering.
Basically--- lots of fabric, 1 yd 1/4" elastic, safety pins, a sewing machine, (serging is faster but you don't have to do this), and some patience.
By the way--- I now make mine with NO elastic. (I've used it all on masks!) The sheets are all perfect, they fit snuggly and wash up perfectly.