In Star Trek, there are several (very) long-range communication devices.
The first of these is the helpfully named “Communicator,” which we likened to a very long-range walkie-talkie. In general, multiple people are available on the connection at the same time, with the exception of a particular call made by Kirk to Scotty, which suggests that it can also be used as a long-range cell-phone-like communication device. In the absence of a method (or even a sound theory) for sending data faster than the speed of light, such technologies are still unimaginably distant; however, over a shorter range (e.g. on earth), cell phones can meet this need. Since we do not have any intergalactic contacts with whom to communicate, there is also little need for such a technology. For astronautical trips to the moon, radio waves can be used to communicate in near-real-time, but the same radio communications made to Mars have a delay of about twenty minutes.
The second of these is the Skype-like audio/visual communication made between Messrs. Spock and Spock and between Capt. Kirk and Adm. Marcus. Conversation-time communications of this sort, as with the communicators, are not necessary IRL over distances such as from Qo’nos to the Vulcan homeworld, and are replaced over short distances by Videoconferencing and some VoIP (Voice Over Internet Protocol) providers, such as Skype.
The issue with producing such long-range communication devices is not with the technology involved in capturing or displaying the data, but actually transferring the data with sufficient speed to enable conversation.
NASA cites the communication delay from Earth to Mars (the time it takes a message sent from Earth to reach Mars or vice-versa) as twenty minutes, which means that the actual response latency (the time it takes a reply from Mars to a message from Earth to get back to Earth) is about forty minutes. The distance from Earth to Alpha Centauri, the nearest star other than our own sun is about 4.4 light years. That means that the communication delay from Earth to Alpha Centauri would be 4.4 years, and the response latency would be 8.8 years. It is truly impossible to hold a conversation when the person on the other end doesn’t hear what you have to say until 4.4 years after you say it, and you don’t hear their response for another 4.4 years.
. NASA/California Institute of Technology Jet Propulsion Laboratory. “Mars Exploration Rover Mission: The Mission.” NASA, n.d. http://mars.jpl.nasa.gov/mer/mission/tl_surface_nav.html, September 23, 2014.