The common cold might be presented as a simple name for a complex process that happens inside the organism, with viral nature. To solve any doubt it's much better to ask a specialist but some knowledge about the subject can be useful.
The usual suspects are between a definite group of different virus with similar characteristics and action but each with unique singularities. It's accepted that most of the time they are rhinoviruses although these with approximately one hundred different, the known number of virus that cause the common cold is twice that. Their objective is the upper respiratory system.
The symptoms for the common cold are sneezing, coughing, headache, throat irritation, watery eyes, runny nose and sometimes others like fever, or created by infections toward nearby zones. It's easy to be confused with the symptoms and think in other cause than the viral character especially when their main activity is in cold, rainy seasons or both. Other possible uncertainty appears with allergies, with several symptomatic convergences.
The infection could be perceived after near one day after the exposure, lasting normally several days with a possible extension of weeks. What about contagion? Well, these little organisms must come from some place! It's always nice to remember how hygiene plays a main role reminding that there are so much possible resting places of viruses —air included— thus cleaning and disinfection are really necessary. With more obvious importance the hands, food dishes, cutlery, areas for handling aliments, clothes, ... Closed, unventilated areas increase the risks.
Of course if you perceive the aforementioned symptoms of the common cold in a person it's better to avoid breathing too close or touching possible sources of viruses. If the person with it —perhaps it's better to say with them— doesn't take the appropriate measures when it touches objects after coughing or sneezing near his / her hands (very usual), or when directing the expired air in those actions, the contagion is almost assured.
They proceed infecting cells until the organism generates a powerful counterattack, specifically designed for the unwanted visitors. Sadly today there is no external cure, only to alleviate symptoms.