Let's examine the fraction 16/24. To reduce this fraction, we need to find a number that divides evenly into both the numerator and denominator. Ideally we want this number to be as large as possible. We call such a number the greatest common factor (GCF). A factor is a number that divides evenly into another number.
Note that there are many methods to finding the GCF of two numbers. Many involve all sorts of "tricks" that truly aren't practical in most contexts. Additionally, it is rare that you will have to reduce an obscure fraction unless it is specifically for practice doing so.
To find the GCF of two numbers, make a list of the factors of each number. Then look for factors that are common to both numbers, and select the largest of those. This is much easier done than said, and with practice you'll be able to do it in your head. In this example, the factors of 16 are 1, 2, 4, 8, and 16. The factors of 24 are 1, 2, 4, 6, 8, 12, and 24. The greatest common factor is 8.
What we do is take the GCF, and use it to divide both the numerator and denominator. We always must divide both by the same number, otherwise we've altered the value of the fraction. Note that by dividing numerator and denominator by 8, we've effectively divided the faction by 8/8, which is 1. Dividing by 1 is always allowed because it doesn't change the value of what you are dividing.
After doing the division, we get 2/3. A quick check shows that the GCF of 2 and 3 is 1, but dividing by 1/1 won't help at all. The fraction is fully reduced. There is no common factor larger than 1.
Sometimes students take a very long time to find the GCF, or they are frustrated if they are having trouble finding it. Understand that it can often be faster to use a common factor which is smaller than the GCF. For example, since both numbers in the original fraction are even, you know that both are divisible by 2. Let's just use that. Dividing top and bottom by 2 we get 8/12. We're not done yet, because 8 and 12 still have a common factor. If you see that is 4, that will save us a step, but you could also divide top and bottom again by 2, giving us 4/6. We're still not done, so once again, repeat the above to reduce to 2/3.
Notice how dividing by the GCF of 8 allows us to do all of the above in just one step, whereas we took three steps doing it in stages. Still, there is nothing wrong with that.
That's really all there is to it. Make sure that you memorize these steps since you will have to perform this task constantly in math, especially when you get to algebra.