Facebook games running slow is a common problem. The games are often small flash based games that you would think would not ever have issues. There are however a couple of leading causes of them running slow, or the Internet slow in general.
First, make sure your software is fully up to date by starting with Windows (or Microsoft) Update. Once that is done, make sure Adobe Flash is fully up to date. The easiest way to force it to the most current version is to remove Adobe Flash completely and then visit Adobe's website and download the latest version. This has fixed issues with flash before and most Facebook games are flash based.
If that does not solve the issue, you probably have a problem somewhere in your registry. Re-installing Flash sometimes will fix it, but if you have been hit with some sort of spyware or malware, you need to get that cleaned up as well. Think of the registry as a giant database telling Windows where to find things. If things start running slow, it is quite possible that there is incorrect information. We need to correct that information.
To start, we take a look for any spyware that might have gotten installed. I recommend Spybot Search and Destroy. It does a good job at doing a deep scan including the registry to search out nasty entries. The registry part is important. Once the full scan is finished, clean whatever entries it finds, particularly those in the registry. This may take a reboot or two if anything is actively loaded or running. Allow it to run at startup once should take care of the rest.
Now that we have removed anything bad that might cause Facebook games to run slow again, we want to make sure the rest of the registry is clean. So to do that we simply download and run a registry cleaner. This will check every key and make sure they are valid and pointing to the correct location. This will take care of anything that reinstalling or the spyware scan was not able to fix.