Folding, Carrying, Storing
If your mask has a nosewire, fold it without folding the nosewire. This will reduce metal fatigue and breakage.
Carry it in a paper bag; this will help it dry out.
If you have used your cloth mask only lightly, and don’t plan to wash it, or if you are practicing extended use of N95s, consider keeping 2 or more masks in rotation. Keep them in paper bags labelled with your name. Minutes 2.27 to 5.0 of this video from University of Nebraska Medical Center shows a paper towel and a paper bag version of how to store.