Select a topic for your contemplative essay, unless the topic has already be selected for you. If you do have a choice, pick something that will make it easy for you to convey your feelings without coming off as mawkish. For example, topics like "Why I like rainbows" or "The death of my first pet" come off as a bit sentimental; but topics like "Why I like the rain" or "My brother" will let you show emotion without seeming overly cloying about it.
Write the first paragraph. Your introduction should give readers some factual background for your topic, but the emphasis should be on the emotions the topic evokes from you. Using basic literary techniques like similes and metaphors, in which a writer compares one thing to another either directly or indirectly, can help improve the impression that you are thinking about your topic on a deeper level. While no specific "thesis" is needed, there should be at least one line summing up your feelings on the topic. For example, "Although I had a great time on my first camping trip, the thought of my brother stuck in bed at home made it hard to enjoy myself."
Write the body of the essay. This can be as long as you need it, depending on the intended audience. Elaborate on the topic, again keeping emotions at the forefront, but without losing sight of facts and reality completely. For example, if you used the sentence given above, your body might relate all the things you did on the camping trip that should have been fun, but the fact you could not enjoy them with your brother made it difficult. From there, you could go on to explain why your brother is so important to you.
Write the conclusion. This should not only summarize your feelings about the things you have discussed in the other paragraphs, it should elaborate on how those feelings have formed your personality and character. Come up with a concluding sentence that is poignant and meaningful, but avoid the temptation to be overly dramatic or clever.