Playstation 1 (PSX) Modding Guide
The playstation 1 is the easiest to mod to enable disk swapping.

Step 1: Open the disk tray, find the touch point
Step 2: Use something to hold the touch point button down. A blob of blue tack works perfectly, but beware, it might get stuck, so try a match stick or spring or something first.

Thats it - that button is the only thing the psx uses to detect if the disk tray is open. The rest you need to know is in the PSX Disk Swap Guide.