On April 3, the Centers for Disease Control and Prevention (CDC) started recommending that everyone start wearing cloth face masks or scarves when out in public in order to protect others. Gloves are another matter.
The reason behind the face mask recommendation is they have found that the virus may be spread by the tiny particles of moisture that are expelled when you cough, sneeze, laugh or talk. Those who have contracted the virus may be contagious two days before they show any symptoms. Some may never have symptoms or only have very mild symptoms and never realize they were sick.
The reason to wear a cloth face mask or scarf is to protect other people from you, as the cloth will catch those droplets before they land on someone else or on a surface someone else might touch.
Gloves do not protect others from you (unless you have an open wound on your hand). Gloves are recommended for health care professionals who use them for specific tasks to prevent the spread of disease. They follow specific protocols and safely dispose of the gloves immediately after the task is complete, and then wash their hands. Health care professionals go through many pairs of gloves as they change gloves for each patient. If you wear gloves into a store, you are still spreading the same germs from surface to surface that you would have had you touched the same items with your bare hands. If you touch your face while wearing gloves, you are spreading those germs to your face. According to the CDC, for the average person, wearing gloves in public is no more beneficial than frequent hand washing.
A real problem is when people who wear gloves in a store carelessly discard them in a parking lot. This means someone else (usually a store employee) will have to clean up the mess, exposing that person to anything that might be on the gloves. And that store employee could be the same person who will be stocking the shelves, touching all of the items the gloved ones later purchase.
If you insist on wearing gloves in the stores, carry a plastic bag in your car so you can safely use it to dispose of the gloves after shopping, and when you get home, put the plastic bag in the garbage. For the proper way to remove gloves without touching the outside of the glove, see the CDC website. And, of course, wash your hands afterward.