There are many communication methods that could be used by an artificial intelligence. Artificial intelligence can be integrated to various things including robots, phones, IoT and many others. Primary ways of human communications are either visual or auditory, therefore an natural way for it to communicate with a human is through voice, text, images and videos. The output does not have to be limited to screens but can be anything from refrigerators to speakers.
Hope this helped.
"How is it possible for it to see and talk to someone?"
OK, unfortunately this is quite vague... but I am going to try my best.
The monitor of the computer really doesn't change the ability for it to communicate. For instance, voice recognition is natural to humans along with visual factors. So sensors involving auditory elements assists the AI with this. Now I commented that the question was vague because you said "there is no computer screen for the computer, ****thus the AI cannot display an image of itself****.
Even though the AI can not see does not mean it can not communicate. Those who are blind still have ways of communication, just in a different manner. Sure, they can not recognize one with their own eyes, but they can by touch, and read with braille. Now compared to AI communication, the braille is to any other form of sensor.
Sorry for jumping all over the place, also I did not mean to offend anyone with my comparison... :/