Should cloth face coverings be washed or otherwise cleaned regularly? How regularly?
Yes. They should be routinely washed depending on the frequency of use.
How does one safely sterilize/clean a cloth face covering?
A washing machine should suffice in properly washing a face covering.
How does one safely remove a used cloth face covering?
Individuals should be careful not to touch their eyes, nose, and mouth when removing their face covering and wash hands immediately after removing.
Source: CDC.gov (https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-sick/diy-cloth-face-coverings.html)