Connect the gnd pin to the gnd on your microcontroller.
Pick one of the following options depending on the type of voltage converter you wish to use
If you are using a 5V regulator:
Connect the rumble wire (grey) from the PS2 plug to the voltage input for your regulator
Connect the voltage output from the regulator to the pico, via the Schottky diode
Connect the ground pin from the regulator to the pico
If you are using a 3.3V to 5V boost converter:
Connect the 3.3V wire (red) from the PS2 plug to the voltage input for your boost converter
Connect the voltage output from the boost converter to the pico, via the Schottky diode
Connect the ground pin from the boost converter to the pico
Programming
Start Santroller with your microcontroller plugged in.
Hit Configure
Click on Add Setting
Find PS2 Controller Emulation in the dropdown and add it
For the Pi Pico, set your SCK, MOSI, and MISO pins
Set your Acknowledge and Attention pins
Click on Add setting
Find and add USB Host inputs
Bind D+
Hit Save
If you plug in a supported controller to the usb port, the tool should detect it and tell you what it is. Most controllers are supported, but things like the play and charge kit won't work over USB.