To run an old educational CD that requires 256 colors and a resolution of 600x480 on a new PC, access the Display Properties and click the Advanced button, then the Adapter tab, and select 'List All Modes' to find the desired settings. Alternatively, right-click the executable of the application, go to Properties, then the Compatibility tab, and enable options for running in 256 colors and 640x480 resolution. The first method is effective across various systems, while the second is specifically applicable to Windows XP.