How can I run an old PC Windows game on modern systems?
The short answer is: it depends on the game. Some games can be run on modern Windows systems without problems. These games are tagged on Abandonware DOS simply as "Windows" games. If a game on Abandonware DOS requires a specific Windows version, the system tag will be, for example "Windows XP" or "Windows 3.x".
A lot of Windows games won't run on Windows 7, 8, or even Vista. What can you do? Well, if the game is available on GOG.com, you can buy it for a few bucks and be certain that it will run on your system. Otherwise, the best approach is to use a Virtual Machine.
A Virtual Machine allows you to run a different operating system in a window on your desktop. There are a lot of tutorials already available that teach how to install and run a Virtual Machine; one of my favourites is this one on How To Geek. For maximum compatibility with older games I suggest to configure Windows XP in a virtual machine. After that, just run your Virtual environment and run your Windows games!