With a common cold, you catch the virus from another person who is infected with the virus. This usually happens by touching a surface contaminated with cold germs -- a computer keyboard, doorknob, or eating utensil, for example -- and then touching your nose or mouth. You can also catch a cold by encountering secretions someone with a cold has sneezed into the air.
A cold begins when a cold virus attaches to the lining of your nose or throat. Your immune system sends white blood cells out to attack this germ. Unless you've encountered that exact strain of the virus before, the initial attack fails and your body sends in reinforcements. Your nose and throat get inflamed and produce a lot of mucus. With so much of your body's energy directed at fighting the cold virus, you're left feeling tired and miserable.
While getting chilled or wet is not a cause of common colds, there are factors that make you more susceptible to catching a cold virus. For example, you are more likely to catch a common cold if you are excessively fatigued, have emotional distress, or have allergies with nose and throat symptoms.
Source: http://www.webmd.com/cold-and-flu/cold-guide/understanding-common-cold-basics