Read through the problem carefully and note of all the numbers mentioned. Assume that all items listed can be matched with any of the other items.
A typical question may read: "Rachel has four blouses, five skirts and three hats. How many different outfits can she make by choosing a blouse, a skirt, and a hat?" Make a note that the numbers you're dealing with are 4, 5 and 3.
Apply what is known as the "counting principle." In simplest language, it just tells us to multiply all the values given. There are 4 blouses, each of which can be paired up with any of 5 skirts. So far, there are 20 possible combinations. Each of those 20 combinations can be paired up with any of the 3 hats. So multiply 20 times 3 for a total of 60 possible combinations.
For any given problem, simply multiply all numbers provided to get the total.
Another example: "For an early-bird special at a restaurant, a person can choose from 3 appetizers, 7 main dishes, 4 side dishes and 5 desserts. How many different meals can be made by selecting one item from each course?" Just multiply 3 x 7 x 4 x 5 to get 420, which is the correct answer.