In addition to being quite common in homes and businesses in industrialized areas on Earth, public Picturephones are also located in areas on Space Station V.
The ones on the station are located in booths with sliding doors and a chair. To use them, the caller inserts a card into a slot, possibly a telephone calling card or a payment authorization card such as a credit card or debit card, or a prepaid phone card. (At the time the movie was made, the most likely cards would have been a telephone company 'credit card'.)
Use[]
Heywood Floyd is observed placing a telephone call to his home in the United States, dialing either 11 or 12 digits. The first digit was clearly not a zero, as is common† on Earth for international phone calls in the early 21st century. It may be that on-station calls were made using a short number, but that calls off the station were made by simply dialing the country code followed by the number, with no prefix digit; if this is the case, then Floyd probably dialed 1‡, his area code and number. Alternately, all calls are dialed in this manner, so an on-station call (e.g. one office calling another on board) would require the caller to dial the station's own country code followed by the local number (probably a three-digit country code followed by a four-, five- or six-digit number).
(† Most countries in the world now use 00 as the international calling prefix; North America uses 011; Russia -- and the Soviet Union before 1992 -- use 8-10; there are some national variations in other countries. Floyd was not seen pushing the zero as the first digit.)
(‡ 1 in this usage, as the North American Numbering Plan (NANP) country code, is not to be confused with the trunk dialing digit of 1 commonly used within the NANP for long distance calling. In this usage, 1 is used to dial into the NANP, 44 to dial into the United Kingdom, 81 to dial into Japan, 353 to dial into Ireland, etc.)