That's quite a broad question, but here are a couple of ideas. I'll start out with a couple of general ways to research, and then below are a couple of ideas that personally I would find more interesting.
First, search for Linguistics Syllabus in your preferred search engine. Check out a couple of course syllabi and look at the topics for the course. Pick a term that looks interesting and search for that. If it looks boring to you, pick another topic from the course syllabus and search for that. Keep doing that until you find something that piques your interest. You could also start with your own course's syllabus if you have one.
Another idea is to check out the table of contents to an Intro to Linguistics book if you have one. If you don't, stop by your university's book store or a local bookstore and write down some of the main terms (not sure if this is for high school or college but either way you can follow the same steps). You could also check out some of the citations for whatever chapter you are interested in to find more sources and then check them out at your university or local library.
Personally, I'm intrigued by how linguistics relates to cognition. Back in undergrad I worked on a study on something called the linguistic intergroup bias. The idea is basically that our perceptions of a particular person or demographic group can be influenced by the words used to describe that person or group. Consider these two sentences to describe the action of a person stealing from a store:
1. The man stole a book from the store.
2. The man is a thief.
Both sentences are negative, but Sentence 2 has broader implications for the man's personality (not just one action, which could have been consistent with his general character or an anomaly). Some studies have found that people are more likely to ascribe more enduring negative language to members of other demographic groups (for instance, if the rater is White, he or she might describe a person of another racial group more negatively than a person of his or her own racial group. The same might go for gender or age. Hence the word bias in linguistic intergroup bias).
If you don't like that idea, another interesting line of research is how word choice affects people's memory and interpretations of the events of crime scenes. You can check out some linguistic and cognitive psych studies. A common example given for this is something like:
1. The red car passed by the blue car and hit the stop sign.
2. The red car flew by the blue car and smashed into the stop sign.
Although they describe the same event, these two sentences give the listener a decidedly different feel about what happened. If you picture a witness testifying in front of a jury, Sentence 2 would give a much more reckless and violent portrayal of the offender, which could in turn influence how the jury interprets later testimony or rules on a case.
Lots of interesting stuff with how words relate to our interpretation of events, people, etc. This might be a bit more advanced than your professor wants if you are in an intro class (perhaps he or she prefers that you focus on the basic building blocks of language, in which case again you could start by checking out the syllabus). But I think the linguistic-psychological connection is more interesting, to me anyway. :)
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