Do I need to use longer or more complicated words to sound more professional?
Surprisingly, no. Professional writing is clear and concise. Avoid jargon to ensure that your readers can follow your points easily.
What's the best section of a study to look at to understand it?
Methods. The methods will tell you the "meat" of the study- what was measured, how it was measured, who was involved, and where/when it happened.
When you're asked to write about a piece of literature from your class, how might you start your paper?
The best way to start is taking good notes. See what themes emerge from sections of the piece you're asked to analyze. When you start to see common ideas, note in the margins what passages support your common themes. From here, you might come up with a thesis if you haven't already. Starting with a thesis can be harder unless you know the material well.