If I understand a throat, it is the area forward of the shell where the rifling is machined out to allow room for the bullet to be before it is fired and engages the rifling.
If that is the case, then how can a smith adjust the amount of throat a chamber has? I would think the reamer would have x amount of throat in front of the shell area and that would be the end of that. If you want a throat of a specific length you would have to have a specific reamer made to those specifications.
Thanks.

You are correct in your assumptions. If you want a standard throat, most reamers are ground to SAAMI specs. If a shorter or longer throat is desired, in the case of a shorter one the reamer would have to be either reground or the throat specified when ordering the reamer, making it a non standard. If a longer throat is desired, then the smith simply uses a throating reamer to lengthen it to the correct length.

Frank,
A lot of smiths have no throat reamers and use a throater or throating reamer to custom fit it to your bullet or seating depth.