Three main possibilities (one or all of them could be contributing): Lack of puppy and people socialization, Lack of obedience training, Lack of exercise (Physical and Mental Challenges).

Your dog needs to know that it is NOT ok to behave aggressively. It's your responsibility to provide him with opportunities to relate to dogs and people politely. He needs to meet and greet people often - and to learn that being friendly gets him attention and praise. DON'T pick him up when he's being a bully - that reinforces the bad behavior. Turn him around - on leash - walk him away from the fun until he chills out and come right back and try again - meet up with dogs you know - not totally strange dogs especially in the beginning - if you have friends with calm tolerant dogs, ask if you can practice with them.

Take him on walks, even though he is little, he needs a real dog walk and to learn to walk near you/ behind you without pulling on the leash.

Enroll in a certified training class specializing in socializing dogs that are highly reactive. You may need to work individually with a trainer until your pooch is ready to join the group - but joining the group is the goal.

You can take a look on Mahalo at clicker training a training methodology based on positive reinforcement that makes training fun for your dog and for you. Also see here for more information on dog obedience training.

The fourth possibility is a Physical or Medical issue causing pain, discomfort - creating pain based warning or fear behavior. If you have not seen a vet in over a year or have a suspicion that a medical issue may exist - please visit the vet to rule out any health issues.

Best of luck to you both - your dedication, putting the time in now will reap rewards down the road - wuf.

I agree with both answers that socialization with other dogs and humans is key. However, be sure that those other dogs have had all of their shots and don't take your puppy to strange places where it can come in contact with dogs you don't know (or their feces), as it can catch some terrible diseases such as Parvo and a variety of parasites that way!

I am a big fan of Bark Busters, as it worked wonders for my lab. They come to your house and teach you how to talk to your dog in a language your dog understands. They guarantee the training for the life of your dog, no matter who it lives with, and can come back as often as you need. You do, however, need to work with your dog daily to reinforce good behavior. Never talk to your dog in a soft voice and say it's okay when it's bad or scared, as this shows you are not the alpha of the pack. Learn more at www.barkbusters.com and good luck!

I'm glad that you recognize this now, because once puppies grow into adult dogs, it can become harder to deal with. There can be many reasons why your dog is showing aggression.

I have owned Chihuahua's for almost 20 years and the biggest problem I see with this breed is aggression, and it's because they're treated like toys. These dogs are not toys, they are dogs and need to be treated like one.
People often hold and carry these dogs too much, making them an extension of their body rather than a separate entity.
They want to be on the ground sniffing and peeing. They are dogs.

There can be so many other reasons for this behavior please look through
Dog Obedience Advise since they have a great page on puppy aggression.
Remember that puppies need socialization too. sign up for a puppy obedience class from your local ASPCA. Good luck!
http://dogobedienceadvice.com/how_stop_puppy_aggression.php