How many stages are there in swallowing?

Swallowing: The swallow mechanism is normally broken down into three phases. The oral phase involves chewing and formation of the bolus and propulsion of the bolus to the pharynx or throat. The pharyngeal phase involves transfer of the bolus past the larynx and into the esophagus. The esophageal phase involves transport of the bolus through the esophagus and into the stomach.

Three main phases: There are three main phases; oral phase, pharyngeal phase, and esophageal phase. There are many components to each phase that you can read about (wikipedia) if you need further details.