He then phones round among the musician contacts, taking into account the need to have a balanced band, with the appropriate range of instruments, and also considering which musicians live nearest to the venue, thereby avoiding long-distance travel. The chances are that all the musicians on his list are already players in other bands, so he can book them only if they do not already have a gig on the date in question.
Such bandleaders and agents are in a sense 'fixers'.
Even some well-known bands are in effect 'telephone bands'. You may notice frequent changes of personnel. This is because the leader has a pool of musicians from whom to choose.
Usually it is musicians who have gained wide experience and met many players over several years who decide to run one or more telephone bands. One - or more? Yes, we have a famous fixer in England who sometimes puts out two or three telephone bands to play in different places on the same date - for example on New Year's Eve, when there is great demand.
Obviously a telephone band is a strange animal, because musicians can find themselves playing a gig with others they have never met before.
Such bands will not have had a rehearsal and the tunes they play will probably all come from the straightforward core repertoire. It is unlikely that any of the musical arrangements will be very complex. But audiences tend not to notice these things.
By the way, a telephone band is in some ways similar to a 'pick-up band', though not quite the same. Pick-up bands are put together for special projects, such as a providing a backing group for a recording, or accompanying a singer on a tour. They are likely to be technically highly-skilled; and they are also likely to rehearse seriously together before undertaking the work.