I have installed this game to Windows 2000 Pro (SP4) and Windows XP Pro (SP2). Well, I did NOT install it for XP... at the time of installing, I got dual-booting system.
Here is how I did it.
1) At first I tried the autorun... no.
2) Then with all compatibility mode... no.
2.1.) Copied whole CD to HD and then tried with all compatibility mode... no.
3) I launched Windows Explorer and started to explore the RA CD...
3.1.) Found two interesting folders... SETUP and SETUP95...
3.2.) Figured out that SETUP95 is Windows version

(no sh* Sherlock).
3.3.) Browsed to SETUP folder.
3.4.) Found two exes, SETUP and INSTALL.
3.5.) Launched SETUP.exe...
3.6.) DOS version of SETUP started...
3.7.) Did not found CD, so I swapped the CD to
PRIMARY CD drive.
3.8.) Retried and SETUP started!
4) I did not choose any sound card in fear it crashes.
4.1) SETUP suggested C:\WESTWOOD\REDALERT, accepted and install started.
4.2.) Success.
4.3.) Browsed to C:\WESTWOOD\REDALERT and used RASETUP. 640x480,Backbuffer,Allow hardware filled bits.
5) Right-click and compatibility tab.
5.1) Choosed Windows 98 / ME and checked ALL compatibility checks.
5.2) Started and ... it worked!
And for Windows XP, I just created shortcut for RA95.exe and applied same compatiblity modes.