The first main identifier is that you are dealing with a word problem, and not just a general equation that they give you. From there you will see the problem asking you to optimize, maximize, minimize, find the minimum of, or find the max of. Basically, words that are asking you to find the largest or smallest amount.
Note : Many people get these problems confused with what are referred to as Related Rates problems (which we will discuss in the not-too-distant future). The key when trying to distinguish between the two types of problems is to note that optimization problems are asking you for a max or min amount of something. It is a fixed value they are wanting as an answer. A related rates problem will ask you about how something is changing. The language will be about how quickly or slowly something is changing. These problems are describing movement.