Here's the good news...you now have an excuse to learn that gaming system and 'play'!
Most gaming systems are internet capable, and while the very young user may not have the ability to set it up, you can guarantee the little bit older one can...so you'll need to take some precautions. Remember, even though you have a secure wireless network at home (you do, don't you?) and the kids don't have the password, the portable gaming systems can go anywhere...and internet may be available for easy connection.
First, let's talk about handheld gaming systems. Originally, they were designed such that you simply put in a game cartridge and you played that game. Then, they moved on to being able to connect with nearby systems and play together. So, two or more friends in the same room could play against each other on the same game. Now, they are fully internet capable. You can play online, download games, but more importantly, browse the internet. On most systems there is the option to disable each of the connectivity features, but there is no option to put in internet filtering...so for the browsing it is all or nothing. My thoughts are that you sould simply disable that feature for kids, they can do their browsing on the home computer. The rest of the features you will want to review individually and decide.
Now, the big systems are internet capable too, or at least anything within the last few of years. I'm talking about the XBox, Nintento Wii, Playstation etc. There are some advantages to them being internet capable because this is the simplest way to get updates to the underlying software which can be important, and you can download movies and new games etc. which will really increase the enjoyment the whole family gets out of the system. But again, with these advantages come the same dangers as the internet anywhere...
For any kind of system you can simply search the internet with the words "parental controls" and the name of the gaming sysem to get the detailed instructions.
How to get started if you don't have a clue?...ask your child! Get them to show you how to 'play' first...that will get you familiar with how to use the controls and navigate a little. They'll be able to show you an amazing amount of things.
So go ahead, play a few games... all in the name of research and learning of course...have fun!