Some have referred to shaking hands as the "Butt sniff of the canine world." To a human, you can tell a lot by the quality of a person's handshake. We notice things like strength of grip, how sweaty it is, and how long the other person holds the shake. Not really that much in comparison to what a dog can tell by sniffing the derriere of another pup.
At the same time, a good handshake can be seen as a sign of an intelligent and polite dog. It is also one of the first tricks the average dog owner tries to teach their dog once he has mastered the basic commands. In general, it is pretty easy to teach and in most cases, can be taught in a few days.
The concept itself is relatively simple: you say "shake" and your pup lifts one of his paws up so that you can take it and shake hands with him. Instead of grabbing his paw, lifting it, and expecting your pup to know what's going on just because you are making him do it, what you really need to do is teach your dog to lift his paw on his own.
You can do this in several ways, but before getting started, you need to choose your cue word. You can use virtually any word. "Shake" is the most commonly used, but you can use anything. The big trick is no matter what cue word you choose, you need to remain consistent during training and afterward. You also need to make sure everyone else is on board with the same cue word.
While it will be much easier if your pup has been taught the four basic commands, 'sit', 'stay', 'come', and 'down', as long as your pup will sit on command, you can teach him to shake. This is because it is much easier for your pup to perform the shake trick when he doesn't need all four legs to stand on. For this trick, you won't need much in the way of supplies. Here is the list of things you will need:
The big thing here is that Chihuahuas are more stubborn than many other breeds. While they are eager to please, it can take a little longer to train your Chi to shake, but the fun you have showing it off is more than worth.