How to run Mechwarrior 2?

It depends on which version of the game you have. If you have the DOS versions, you can try running it using a DOS emulator called DOSBox. Keep in mind that the game does not support 3D acceleration when run out of DOS, it supports software rendering only with that setup.

If you have the Titanium Edition discs, you are probably out of luck, as those need Windows 95 or 98 to run. Windows XP and newer will not run the Titanium versions of MechWarrior 2. If you have the Titanium versions, you are probably going to have to either build a legacy computer just to play the game, or you will have to explore running Windows 95/98 in a Virtual Machine, and hope you can get the game running well in a virtual environment. Windows 95/98 will not run on modern hardware, so dual booting into an older OS is not an option unfortunately.