Process Analysis Technique
As noted earlier, "analysis" means to break down into smaller parts.   A process analysis does exactly as it implies; it breaks down a process into smaller steps.   Another name for a process analysis is a how-to paper.   Anytime you've ever written down a recipe or directions to a location, you've used this method.  
There are two types of process analysis:   informative and directive.  

In a directive how-to, you are instructing your readers to follow certain steps. This often involves addressing the reader directly with the imperative verb tense.  In other words, you give commands directly to your reader in a directive type of process analysis.  

Example:  "How to mess up on a first date:   Show up late.   Don't apologize.   Check out other members of the opposite sex while pretending to listen."  etc etc

In an informative how-to, you don't so much direct your reader as explain how something is done or what takes places during a certain process.  

Example:  "Yosemite Valley was created by a series of glacial movements over time."      

Knowing which type of process analysis to use will definitely influence your choices during the writing process.

Tips

1.  Understand the process:  In order to illuminate your ideas about a process, you must first understand how it happens or happened, and in what order the steps come. 

2.  Consider your thesis:  What is it you want your readers to know when they are done reading your essay?  If your process analysis is a recipe, then the outcome is obvious - you want your readers to have prepared a successful dish.  An academic process analysis should be just as focused, but with the added bonus of having some insight about the topic revealed in the process. 

3.  List all steps:  Make sure you haven't left anything out. This is particularly important for a directive process analysis.  It should be thorough and detailed from beginning to end.  Be sure to include transitions, or markers that delineate one step of the process from the next. An outline might be particularly helpful when writing a process analysis.  You can test the thoroughness of your analysis by showing it to someone who is unfamiliar with the process you're describing.  Could your reader complete the process successfully using only your directions?  If your essay is informative rather than directive, does the process unfold clearly?  What questions might be left in your readers' minds?

4.  Define any unfamiliar terms:  This seems self-evident, but many people don't think about it. 

Further resources for Process Analysis Essay
What to Consider When Writing a Process Essay - LEO St. Cloud State University
Process Analysis Essay - Kamehameha School