Wire the joystick

Four buttons with a lever

To the mainboard, the joystick is four more buttons: UP, DOWN, LEFT and RIGHT are sockets like KEY1 to KEY10, with the same resistor and the same V(MCU). Each microswitch goes on one of them with one of the two-wire cables.

The switch on the far side

The handle pivots in the middle of the housing. The part below the pivot, the actuator, moves the opposite way to the handle, and it is the actuator that presses the switches. Push up and the actuator presses the switch at the bottom, nearest you.

So wire the switch nearest you to UP, the far one to DOWN, the one on the right to LEFT and the one on the left to RIGHT. Then check with the input monitor rather than trusting the picture: push each way and read the name it prints.

UP pressed
UP released
LEFT pressed
LEFT released

The three tabs

Each microswitch has three tabs, usually marked COM, NO and NC. Use COM and NO: normally open, closed only while pushed. NC is the opposite, and a switch wired to it reads pressed until you push the stick.

Diagonals

Push the handle into a corner and the actuator presses two switches, so the monitor prints two directions. That is what a diagonal is. Whether your game treats it as a diagonal or keeps only one direction is a decision for the code, not the wiring.