The most common way of gaming on Linux is by using Wine
. This is a free program that will help run Windows programs. Either look in your package manager for WineHQ or go to their website to download and install the program. One installed, just open the exe or setup files in wine and install the game like normal. If there are some performance issues, you might have to configure Wine and run it under a different mode. Generally speaking on the WineHQ website there are ratings. These will give you a good idea of how well the application will run. If it has a very low rating, don't get your hopes up that the game will work well or not.
There are also some paid services that will help you install and run Windows games. Some like using these because it makes it really easy. Others do not like the idea of paying money to run applications on a free operating system. Most of these will run the more popular games that people are buying. For the most part these work pretty well although not every game you want will work.
There are also quite a few open source games that are ported for Linux. These are not your commercial Windows games by any means, but quite a few of them are fun. Some are even clones of older classic games that people have enjoyed like FreeCiv. If you try and hate them, it's not a big deal since they are completely free.