I just found an advisor, and the semester after that, I took a much harder courseload because I'm behind on my course requirements. As a result I haven't gotten a lot of research done. Is my advisor going to regret taking me or think I've somehow deceived him?
Communication is critical here. If your advisor knows what you are doing and why you are doing it, there is a much better chance that he or she will be patient with a low rate of progress.
You can communicate in a number of ways. A sit-down talk is obviously the most straightforward, but you can back up the message by putting in face time time in the office or lab, attending all lab meetings and relevant seminars and departmental events, and so forth. You can even ask for advice on how to balance classroom and research time. Sometimes an A- and research progress is better for your education than an A+ to the exclusion of everything else. (See also the threads about the relevance of your PhD grades going forward).