Both Aztecs and Mayans had strong religious beliefs and well developed cultures. Both had agricultural development though the Mayan may have been superior. The Mayans had a decided hierarchy in government with high positions going to upper class men while the Aztecs had less sophisticated structure.
In addition to the advice offered in the prior posts, a brief but informative introduction followed by a thesis statement will convey your knowledge of the subject matter and the purpose of your essay. For example, you can identify the Maya and Aztec empires as two of the four great civilizations of mesoamerica. Create a point of reference by stating the time periods and geographic location of each. (enotes can provide you with tremendous resources)
The thesis statement describes what you hope to prove in the essay. In this case the political,economic, social similarities and differences between the two civilizations.
I would just reiterate what others have said, namely that A/B A/B usually contributes to a much more sophisticated and analytical comparison and contrast. As far as actual content to focus on, I would focus on some of these analytical categories: the organization of Mayan and Aztec political systems, their diplomatic relationships with surrounding Indian polities, their religious systems and cosmologies, their social hierarchies, in particular how stratified they were, the types of agriculture they practiced, and perhaps the technologies they used. Again, use your own words, and if possible, use some primary sources- especially Spanish sources and perhaps even archaeological evidence. Don't just regurgitate what is in textbooks and encyclopedia.
I agree with #6. I personally find that the A/B A/B format gives a more coherent final essay than other approaches, and it means you have a more focused approach on the key areas of similarity and difference than if you just spent one paragraph describing one civilisation and then another paragraph devoted to the other civilisation. In addition, I think you need to clearly define your thesis statement and make sure you introduction effectively signposts your main points.
Since you don't tell us the expected length for your completed paper, it's hard to know what to suggest about the amount of detail you should include. If I were reading your essay, I would prefer that you use what post #2 called the A/B A/B format. This means that you would describe one type of social characteristic in the Aztec society, then immediately compare and contrast it with the corresponding characteristic in the Mayan culture. This will probably give you a longer finished essay than if you described all the characteristics of one culture in a block, then covered all the information for the other group.
A simple way to organize ideas for comparison/contrast is to either make lists or use a Venn diagram. This diagram involves drawing two circles that overlap each other in the middle. In the separate areas of each circle, write characteristics of the Mayans in one and characteristics of the Aztecs in another. If any of these characteristics are the same transfer them to the central area shared by both circle--these are the traits that are the same. The others in the two last parts are the ones that differ.
The thesis can be as simple as stating that although the civilizations of the Mayans and the Aztecs both have similarities, there are several ways in which they differ. Refer to a writing handbook for a list of transitional words such as similarly, unlike, on the other hand, in contrast to, etc. that will assist you in putting together a coherent essay. Good luck!
Another helpful resource is the Online Writing Lab at Purdue University. This has all the information you need for proper format, sourcing, and citations. These are very important parts of any essay; when you have completed your research make sure to cite all your primary sources. There are different formats for books, encyclopedias, online sources, video and TV, transcripts, etc. Make sure you use the correct formats for each. As #2 says, do not copy anything word-for-word unless you are specifically quoting; you must be coming to your own conclusions in your work. Citations are the best way to avoid plagiarism.
As noted above, there is very sufficient information on the Internet regarding the social and political patterns of the Mayans and Aztecs. The proper way to begin any essay is to create an outline, which helps you to logically categorize your information. A point-by-point Comparative Essay would outline like this:
II. Social patterns of Aztecs and Mayans
III. Political patterns of Aztecs and Mayans
The introduction should let your reader know what the purpose of your paper is without getting to specific (specific examples should be left for body paragraphs). In both body paragraphs, be sure to provide ample examples regarding the social and political patterns of each group. The conclusion should restate the main points of the essay (without saying exactly what was said already).
Since you have to write an essay on this topic, the first thing you need to do is some preliminary research. Fortunately, there is a good deal of information available about this topic, both in the library and on the internet. Also, if your school has any databases available, you should definitely check those. It would be helpful to know how long the essay has to be and how much detail is required. There are two basic ways to set up a comparison and contrast essay:
AAAAA / BBBBB
A/B A/B A/B A/B A/B
Once you've done your research and have decided which topics you'd like to focus on, we may be able to make some more specific suggestions. Remember that it's important to cite all your sources and to copy nothing. Students sometimes forget how greatly teachers dislike plagiarism and how easy it is to discover plagiarism these days. Sometimes students plagiarize without quite realizing that this is what they are doing; if you ever have any questions about what does and does not constitute plagiarism, never hesitate to ask your teacher.
Good luck with your research!