Both Java and Flash are available with Linux. If these are the requirements to play these games, you shouldn't have a problem. I've never played the games on facebook, nor do I have a pogo account, so, I can't attest to this personally, but, I have not found anything online that runs from a browser (like firefox) that I can't use in Linux.
Edit: I just looked at the pogo site and a lot of the games have to be downloaded. I couldn't find requirements as to what operating systems they cover, but, most of the games are .exe files, which are windows only files. You might be out of luck running them on Linux. An application called Wine allows you to run windows apps on Linux, but for a newbie, I'd stick to running them on windows. Just my 2 cents.
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Edit: I just looked at the pogo site and a lot of the games have to be downloaded. I couldn't find requirements as to what operating systems they cover, but, most of the games are .exe files, which are windows only files. You might be out of luck running them on Linux. An application called Wine allows you to run windows apps on Linux, but for a newbie, I'd stick to running them on windows. Just my 2 cents.