There is a free demo version of Syndicate Wars.
The demo contains one mission: The Eurocorp mission in Tokyo, where you have to kill all Unguided and persuade the professor:
Download Syndicate Wars PC demo (12MB)
You can run this demo on new computers in the same way that full version - read "New computers" section for details.
Since the game is an Abandonware, you can get a full version for free. Many versions with animations ripped out are available on the WWW.
To get a full version containing all the animations, or the Playstation version, you will need an emule client. The best solution is to get a full ISO image.
Full, multilingual ISO PC version with all animations but without audio tracks has about 370MB. You can download audio tracks on this site, in Sound gallery section.
Full multilingual PSX version (pal) has 290MB and have built-in music tracks.
Note that in the law, there is no such thing as Abandonware. Downloading and using any copyrighted game without paying for license is a violation of law. But since the game is no longer in sale - this is the only way to get it.
I can't give you the game through this page, because I have upload restrictions on this server. It should be easy to find the game anywhere else.
The original game package contains a manual.
You can get this manual in "Game manuals" section.