I have a blue crowned conure that is extremely conversational; he uses words and phrases in the right context. I never intentionally taught him to speak, but I use the same phrases with him every time. He has picked up many of those phrases and uses them correctly.
Some people use tape recorders to teach their birds to talk, but I think that encourages mindless repeating ("parroting") without true comprehension. Talk to your parrot and use the same phrases every time.
My conure likes to say, among other things:
Do you wanna go night-night? (when he wants to go in the cage and have it covered)
Do you want some nummy num? (when he wants something to eat)
Go in the cage. (when he is calling the other birds to go in the cage with him)
Julian go bye bye? (when my son is gone)
Shhh. Stop, no no no no (he says this after screaming for a few minutes)
Good luck
and have fun...your bird may just start a conversation with you out of the blue when you least expect it!!
