The most important thing to remember about transitions is that they express to readers how your thoughts relate to one another. They are like signposts for the road that is your essay, like bridges that join the islands that are your paragraphs, or like links that join the chains that are your sentences. In other words, without them, readers will become lost and confused, wondering how you moved from one idea to the next.
Therefore, to learn where to put transitions, you must first learn to see the discrete parts that make up your entire essay, your paragraphs, and even some of your sentences because you need transitions where those parts come together. In fact, perhaps the most familiar point of difference in writing is whenever you start a new paragraph, which must start with a transition to show how the new paragraph builds on what you just said before.
However, to choose a transition, you must first understand how the old and new ideas connect to each other: do they agree, disagree, cause or effect each other, follow one another, state an idea then give an example, etc.? Once you understand how the ideas connect, you can then choose a transition of the appropriate category. You can also see examples of transitions colored blue in this answer!
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