Phone ringers (what normal people call "bells") generally have four wires, coming from each of two coil windings.
Two wires (one from each winding) connect to a capacitor inside the network circuit, via terminals K (slate color wire) and A (slate with red stripes). This puts the capacitor in series with the ringer. The capacitor passes AC which is necessary to ring the phone, but keeps DC talk power from reaching the ringer.
In modular phones, the other two wires are attached to the L1 (black wire) and L2 (red wire) terminals on the network, and connect to the green and red wires (or white/blue pair) in the phone jack.
In older hard-wired phones, one wire (black) from the ringer was attached to the G terminal on the network, where it met the yellow wire in the line cord.
At the terminal block, green and yellow wires were put on the same "G" screw to connect to the green wire in the wall.
To update an old hard-wired phone, take the black ringer wire off the G terminal in the phone and put it on L1, and attach your modular line cord to L1 and L2.
(Some wires were removed from the network in the photograph to make it easier to see the ringer and line cord connections.)
Some phone ringers have just two wires. Typically, one goes to L1 and one goes to K. There should be a connection from A to L2 either with a jumper wire or via the hookswitch.