Can you teach a sun conure to talk?

Start your training by repeating a simple word to your conure. For example, you can say "hello" or "hi", or you can repeat its name. Repeating this same word, in the same inflection, will allow your bird to study the sound you want it to mimic. A conure's first words should be short, about one or two syllables.

How many words can a sun conure say?

A sun conure could probably pick up a vocabulary of 5-10 words. Of course it could be more or less, it depends on the bird. From personal experience, smaller parrots like conures that don't have a talking ability like a grey, will probably pick up something you don't intend for him to start saying.