Here's the gist of the game: each card in the 81-card deck has between one and three images on it. These images come in three shapes (diamond, oval, and squiggly), three colors (red, green, and purple), and three levels of shading (solid, lined, and empty). Every possible combination is available on one single card.
The goal is to find sets from a collection of cards laid face-up on the table. A set is any three cards where each of these four features are, independently, either all the same or all different? So, a single red solid diamond, a single green solid diamond, and a single purple solid diamond make a set (in that example, the number, shading, and shape features are all the same while the colors are all different). Also, a single empty purple squiggle, two lined green diamonds, and three solid red ovals make a set. Got that? Good. If not, click through the gallery of images from the app starting here to see how the game's designers explain things.
If you want to give Set a try for free, you can try an online daily puzzle here, or download the very limited lite version of the iPhone app here. For learning the game, the app's tutorial is tremendously helpful. Keep reading to find out more about how the game works, or doesn't, on the iPhone.