Democracy 2 is not a demanding game in terms of graphics, and most modern video cards will have no problems at all. If you do encounter problems, the very first thing to do is make sure you have the latest drivers for your video card (check here). This is a cliche exactly because it *is* true, so many bugs are driver bugs.
The game writes a lot of debugging information as it plays to some text files, to ensure we can track down any problems. If the game showed you an error message, but you forgot it, you can email me the right files instead. The debug files are inside the games \debugdata folder, wherever you installed the game (probably C:\program files\democracy 2). The files in question are 'debug.txt' and 'drawdebug.txt'. ignore the rest of them.
The first place to look for tech support is our forums (click here) where you will find discussions of existing bugs, fixes for bugs, and common solutions, workarounds and explanations. If you don't find what you need there, you can of course email me (the programmer and designer) here