Games are one of the most familiar mediums in which reviews are written, so this should feel pretty familiar. Reviews themselves are easy, too, especially compared to comics. The one interesting thing about reviewing games is that the price also has to be taken into account, partially because it varies so much, partially because the quality is often proportional to the price, and partially because they're often quite expensive. Anyway, on to the criteria.
Story: Is the game's story any good, and should it be? Have the developers and writers made a conscious effort to create a good story and is it relevant to the gameplay? This criterion will judge both the plot and the world that the game creates, as well as its characters and settings. Now, many games won't even have a story, and many don't need one. Of course, when you have a good story where you don't expect to find one, you tend to like the game more, so the story is still a relevant criterion; however, the weighting of this particular category will be related to how important the story is to the particular genre.
Visuals: Does the game have good, original, interesting visuals? Are the standards of the current generation, the console, and the price met? You'll notice I used the term 'visuals' and not 'graphics', because 'graphics' tends to imply only the objective quality and complexity of the game's visual characteristics. As any real gamer will tell you, however, games don't need good graphics to succeed. 'Visuals' refers to a combination of graphics, art style, neatness, etc. Visuals aren't the most important category, but they can greatly enhance a game, and also bring it down a few notches. This latter usually occurs when the game has serious flaws in its visuals, from plain ugliness to technical issues (particularly relevant for PC games).
Audio: Music, sound design, and voice-overs are all judged in this category. Again, not the most crucial element, but one that still serves to greatly improve a game. Bad voice-overs and sound effects can also hurt the game.
Gameplay: The most important factor, obviously, but also the hardest to judge. Gameplay varies infinitely from game to game, so judging a game's worth is only really possible by the entertainment factor and a comparison to peers in the genre. This criterion will be weighted the most in almost all cases, as it is what defines a game; all else can fail, but a game with good gameplay will be remembered for a long time. Creativity and originality are also important; not referring to being an original title (that would be way too harsh given that most major titles are sequels...), but rather ingenuity in gameplay design.
Replayability/worth: Another important factor, this mostly determines whether someone should buy the game at full price, or wait for a sale. Of course, many games don't necessarily need hundreds of hours worth of gameplay (quality over quantity), but some titles really do skimp on the 'content' part, which means that, even if they are solid titles, they're usually not worth the full $60 from the start.
Especially with games, it's worth noting that each category will be weighted quite differently between titles. Also, pay attention to the Replayability/worth criteria if you're on a budget; as I said earlier, even great games may be overpriced.
That's it for the intros; I'll be posting a short list of upcoming reviews and what to expect, then I'll jump right in. As always, criticism and comments are more than welcome, just be civil :-)