You are most likely to get a cold if someone sneezes or coughs over you or near you. To avoid the spread this way, you need to stay at least a 6 foot diameter distance from the person. Cold viruses are in the air on respiratory droplets for a short time after a cough or sneeze. Although they can travel in the air for only a matter of seconds and for only about a six foot diameter around the person who coughed or sneezed before they drop out of the air onto surrounding surfaces, that is still one of the most common ways to catch a cold.
So, being in a crowded public area where you can not stay at least six feet away from others is one of the most likely ways to catch a cold, besides direct contact with the person who has a cold (shaking hands, touching their skin, sharing eating utensils or kissing) or contact with things they have just contaminated.
You can also catch a cold from someone else by touching their mucous membranes or picking up respiratory droplets on your hands that have been ejected with a cough or sneeze and then touching your own nose, eyes or mouth, even hours later. Keep your hands washed frequently and avoid touching your face, especially the mucous membranes of the eyes, nose and mouth, and you will more likely stay cold-free.
You can also pick up viruses by touching somewhere a sneeze or cough has touched, e.g., a sick person's hands or used tissues or a nearby counter top or phone. Colds are spread when the viruses enter the body through mucous membranes, typically of the eyes, nose, and mouth. Any transfer of body fluids between an infected person and a healthy person (e.g. a sneeze, a kiss, a shared beverage) can spread a cold. Also, a person with a cold can contaminate a surface such as a table, phone or doorknob with her hands. If a healthy person touches that contaminated doorknob and then rubs her eyes or nose or eats with her hands, she can get the cold. For this reason, regular and thorough hand washing is recommended especially during cold and flu seasons, see the related question below on how to properly wash your hands to remove germs.
You can spread a cold by going to school or work or out in public when sick. It is best to stay home and rest to get well, rather than take the virus in public and make others sick, too.
For even more detail, see the related questions below.