Before you get too worried about your Chihuahua barking, keep in mind that it is his only way to communicate with you and the rest of the world. What you should be worried about, is if your tiny terror barks excessively. While you may never be able to completely stop your pup from barking, you can teach him to be quiet and keep his desire to bark to a bare minimum.
In part, it is also up to you to determine when your Chi is barking for a good reason like he needs food or water or to go outside, or if he is just barking to hear his own voice. He might also be barking to let you know there is an intruder or stranger in the house. One thing to keep in mind is that your Chi will not respond to negative or punishment type training methods, they will just make him dig in his heels and refuse to do as he is being asked.
Since you are trying to teach your puppy not to bark like a crazed tiny terror, the first thing you need to do is learn why he is barking. Keep in mind some of the reasons he is barking are justified, while others are totally not. Once you have a better understanding of why he is barking, you can start working on correcting his behavior.
You should also keep in mind while you are trying to figure out why your fuzzball won't stop barking, chances are pretty good the at least he thinks he is barking for a good reason. The biggest thing to remember is that you need to remain consistent, keep working with your Chi until the only time he barks is when it is acceptable for him to do so.
For this one, you may want to wait until after your pup has mastered the four basic commands of 'come', 'sit', 'stay', and 'down'. This way, he has already accepted the fact you are the Alpha in his pack and are responsible for teaching him in the same way his mother would do in the wild. You won't need much in the way of supplies to train this skill. But, you will need a large supply of his favorite treats and tons of patience.