Phone booths are used by prisoners to reduce their family need by calling their family. If you have enough phone booths, visitation rooms aren't even needed. However, you will need many phone booths, as only one prisoner can use them at a time, and they will talk on the phone for quite a while. Without visitation rooms, 1 booth per 5 prisoners should be enough. With visitation rooms, 1 per 15 or 20 prisoners is probably good.
Prisoners will use phone booths during Free Time regardless of what room they're in, so long as the room is not marked Staff Only in the Deployment screen. Placing phone booths in your canteen is a good idea, since it's likely many prisoners will finish eating before the Eat time is finished.