This is just another lost art (traditional phones are either dead or are instead IP) that I once learned a fair bit about:
The name varies regionally (I've heard them called Centronics, cinch, and CHAMP; though around here, we call them Amphenols). The Easy Method is the same regardless of name: It centers around a split (aka "50 pair") 66 punch block[1] that is mounted to a wall, or to a wall-like object.
Buy a pre-terminated 25-pair cable with the right connector on at least one end, and punch that down in order[2] on one side of the 66 block. That connects the system to the punch block. Importantly, those wires never get touched again.
Phones (or more precisely, wires for jacks for phones) connect to the other side of the 66 block. Those wires also never get touched again.
The two things (phones, systems) are connected/disconnected with bridge clips that combine the two halves of the block (which only allows 1:1 ordering, but that's often just fine).
Alternatively, a "we fancy!" variation uses single-pair cross-connect wire so that arbitrary phones can quickly be connected to arbitrary system ports -- maybe on completely separate blocks.
After that, plug in the Amphenol. Plug in the phones. Have fun talking to yourself.
(Or, at least: That's an easy way for small stuff. Bigger stuff (hundreds or thousands of pairs) eventually really wants better organization, but punch blocks are still normally the order of the day there, too.)