We'll look at a GPA calculation first. Take your first score and multiply it by the number of times that it "counts." For example, a college grade of A- might be considered a score of 3.7. If the class was three credits, then that score "counts" three times. Multiply 3.7 times 3 to get 11.1, and put that number aside.
Do that same step for your other courses. For example, you might have a C+ in a 5-credit lab course. That will pull you down quite a bit. If the C- is considered a score of 2.3, multiply it by 5 to get 11.5. That's not much different than the 11.1 from above, but it will bring down your average more than you'd like because it will count 5 times in the upcoming calculations.
Continue doing this with all of your scores. Multiply each score by its "weight," or how many times it counts.
When you're done, add up all of the products that you put aside--the products that you got by multiplying your scores by their weights.
Add up the number of "weights," or the total number of times that your scores counted. In the case of GPA, that equals your total credits. For example, your sum of products might be 435, and your total credits might be 128.
Take the sum of your products and divide it by the number of "weights." In the example above, we would take 435 and divide it by 128, giving us about 3.4, which in college would probably translate to a bit higher than B+. Your weighted average tells you what you averaged per weight, or in this case, per credit. It's as though you got a B+ in every class.
Let's try a weighted average that might be used for a high school class. Imagine you will take 10 tests for the year. Eight of them are regular tests. One of them is a midterm that counts twice, and one is a final that counts three times.
Since the regular tests count once each, we must multiply each of those grades by 1, but that has no effect. We will multiply the midterm grade by 2, and put that product aside. We will multiply the final grade by 3, and put that product aside.
Now we must add up our products. We'll add the one from the midterm, and the one from the final, and then the 8 from the regular exams that just got multiplied by 1 and didn't change.
Now take that total, but don't divide it by 10, even though only 10 tests were taken. We have to divide it by 13, which is the total number of weights: the 8 regular tests, the double-value midterm, and the triple-value final.
The result of that division is our weighted average, which takes into effect the higher weights of the midterm and final.
Remember that not only should you know how to do this just to compute your own average based on different grade scenarios, but many test questions actually ask you to do this for sample data. Make sure you are comfortable with the procedure.