Talking ability depends on the species as well as the individual bird. Some species of parrot are known to be talkers but that doesn't mean that you can't teach others to talk as well.
Teaching a parrot to talk takes a lot of patience. It usually involves repeating a word or phrase over and over again. Your parrot can also pick up other things as well without any reinforcement at all. It is really up to the individual bird.
You can teach birds to say things on cue. Certain intelligent species, such as African Greys, can sometimes use phrases in context without being cued. Parrots can also learn whistles and noises as well.