A basic clarinet will consist of four major pieces that connect by cork-lined joints, as well as a mouthpiece, which is made up of several smaller components.[1]
The bell refers to the very bottom, cone or bell-shaped part of the clarinet.
The lower joint stalk is the biggest piece of the clarinet. It should have metal keys on the right side of the instrument when oriented correctly, with a bridge key pointing up toward the upper joint. The best way to distinguish between the lower and upper joints is that the upper stalk will have two cork connections, called tendons, while the lower will have one lower cork joint and a metal ring around the upper joint, which marks the center-point of the instrument.
The upper joint stalk will have keys on the left-hand side of the instrument and should be slightly shorter than the bottom joint. Oriented correctly, there should be a bridge key hanging over the connection point at the bottom, and some space between where the keys end and the top of the upper joint, where it connects to the mouthpiece. In other words, you'll know you have the pieces lined up correctly because there should be no keys at the very top or very bottom of either piece.
The barrel is a short section of the instrument that basically connects the top joint to the mouthpiece. There are no keys on the barrel, and the barrel will often be stamped with the brand name of the instrument.
The mouthpiece consists of the black mouthpiece housing, as well as a metal ligature, which is used to hold the reed in place on the mouthpiece. Many clarinets also come with a metallic mouthpiece cover, used to protect the mouthpiece in the case.