You can try the following to see how well a game may run on your computer:
- Input your hardware on PCGameBenchmark and look up the game you wish to play.
- Most popular games can easily be found on the site.
- The site provides a simple "yes or no" answer essentially on whether or not you can run the game.
- Look up a YouTube video of the game you want to play and the hardware you have. This isn't always going to work, but for more popular titles and more common hardware, you should be able to find some videos to give you an idea of what the game looks and runs like.
- Try Can you Run It? as this answer says. This is similar to the PCGameBenchmark site, only it runs an applet to get your hardware information. Additionally, the site can make some recommendations on what "things" can run the game you are interested in.
- Adhere to the "minimum" and "recommended" hardware specifications supplied by the game developer.
- Most games have a minimum and recommended list of hardware requirements in order to play the game. Steam is very good at listing these details, but a Google Search should also point you in the right direction.
- A general rule of thumb is if your hardware is equal to or better than the recommended list of hardware, you should have no issues running a game (at a "playable" experience).
- If you only meet the minimum requirements, the game will still be playable, but at a degraded experience (you'll likely need to tone down some graphical settings).
Also take note of one important distinction, as this answer points out: Running a game versus is the game playable are two different things. What you are really want to know is "is the game playable?" Most systems can run a game on most hardware, but the game play experience will vary dramatically.