There are two main types of bodycords, those used for épée, and those used for foil & saber. All bodycords have the same end that connects to the reel, one with three prongs as pictured below:
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The letters 'A', 'B', & 'C' correspond to the wires on the other ends of the bodycord. The 'A' line goes to one of the blade wires on an épée, and for foil & saber, is the line that ends in the crocodile clip that connects to the lamé.
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Épée bodycords have the same type end that connects to the weapon's socket.
Foil & saber bodycords have many different types of connectors, the most common ones being these:
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The connectors pictured, left to right, are the French (Leon Paul), German (Uhlmann), Italian Bayonet (Negrini), and the Leon Paul Bayonet. Other connectors are known to exists, and some people make their own bodycords using other retaining devices (I have heard of a few people using BNC connectors), but again, these are the most common available.
In foil, for the French and German style connectors, the 'B' line goes to the thinner prong, the plug which the blade wire is connected to. The 'C' line prong goes into a plug which is grounded to the socket, closing the circuit between the 'B' and 'C' lines while the tip is not depressed.
In saber, the 'B' line is not insulated, and the two prongs are both ground to the socket, permanently closing the circuit.
For épée, the 'B' line plugs into the socket connected to the second blade wire, while the plug for the 'C' line grounds out to the socket. The circuit on an épée is normally open while the tip is not depressed.