How do you train your puppy or dog not to bark excessively?

I had a puppy named Freya, and she was really good... but she barked too much. She would bark at little things, and I was in an apartment at the time. She would FREAK if I put her outside on her chain and left her there, and I was told the best thing was to ignore her. But my neighbor got mad and told me that if I would just train her, she wouldnt bark, as though I haven't already tried! When people are babysitting her, she becomes a problem for their neighbors too, howling like crazy when she was left alone. I know this is because she doesnt like to be alone, when she was a puppy, she was hardly ever left alone at all. But I don't know how to train her to not bark.