IMPORTANT: The optional launcher and configuration tool require the .Net 2.0 framework. Try running these programs, if running them fails at startup try installing the framework. You will most likely already have this framework installed as it's used by a lot of software.
Getting Red Alert to work with Linux is really simple. The following steps are required:
Run RedAlertLauncher.exe under Mono. If it doesn't work run under Wine ra95.exe directly or cncnet.exe for online play.
That's it, enjoy!