Birds talk because they wish to communicate with their flock, meaning you, in the same language you use. They are remarkable in being able to adapt this way. If you establish that the language of communication is talking by talking in their presence constantly, then it's more likely they'll be encouraged to try it.
Don't limit yourself to "hello" and "good bye". Just get in the habit of speaking and babbling at them as you hang out. Don't be afraid of looking like an idiot talking non-stop to a bird, either. It's pretty much inevitable.
Sometimes, especially when they're still learning how to talk, they won't speak when you are in the room, because you are already there. Some birds are more prone to speaking when no one is present, because they are calling out to you and trying to get you to come over. You could be around the corner, or you could simply not even be in the house. If you are lucky enough to just be around the corner, this is a good time to reward speaking by returning the call with the same word or whatever. Not only does it reinforce speaking, but it also discourages screaming. You are in essence replacing their normal contact calling with words.
Try to be animated when speaking to them because they tend to pick up inflections before mastering the actual pronunciations. Also, put words into contexts, and they'll understand better and probably be more inclined to pick it up as well. It's uncanny how capable they are of putting words into context. When my GCC came to me, he would lunge and say "don't bite" very firmly while puffed up and looking challengingly up at me. Later, when I taught him to "come here" when I tapped on the cage, he would learn to climb to the top of the cage instead and say "come here". Sometimes when he steps up, he'll say "good bird". When I smile, he'll sometimes mimic my laugh, which actually sounds really evil when he does it.
The most animated words are the ones they tend to find more enjoyable. So, don't swear around your birds, especially when you mean it, and are angry. Also, remember that if you baby talk to them, they'll learn the words in baby talk. I personally don't mind, as I think this is cute. I actually find birds that can speak in normal human voices a bit freakish, especially when they go at it non-stop. They'll also learn words in the voice that the speaker says to them. So, if a woman teaches it to say "hello", the bird will speak in a woman's voice, and vice versa with a man. This might not be clear with birds that cannot mimic well, though.