Adobe quickly responded to the issue, saying that the vulnerability is fixed in 188.8.131.52, the latest version of the player, so to make yourself secure, all you need to do is update your Flash. To check what version you are running, go to this Adobe page. Keeping your software up-to-date is one of the best ways to close security holes; if you're truly paranoid, you could always go the route of adding Flashblock and/or No-Script into your browser. And be sure to keep an eye on our new Azeroth Security Advisor column for more tips on how to keep yourself from being compromised. Once again, to update your Flash and patch this vulnerability go to Adobe's "Get Flash" page.
Update: It is possible that certain versions of 124 (namely, the standalone version for Linux and the standalone version with debug capabilities for Windows) are also affected by the exploits. At this time it is recommended to disable Flash if you are running those versions.
Update 2: It is currently believed that all versions of 124 are safe. Nevertheless, caution is generally a good idea.