Volunteer for medical and psychology studies. Check at the local university and inquire if any medical students or researchers in the psychology department are conducting brain hemisphere tests.
Go to the library and research materials available about left-brain and right-brain predictions. Ask the librarian for recommendations. Do some paper and pencil self-tests and see where you fit.
Watch the right-brained/left-brained dancer on YouTube. If you see the dancer moving counter-clockwise, you are more left-brained. If you see her moving clockwise, you are predominantly right-brained.
Research online tests for dominant hemispheres self-tests. These tests are generally a choice of one answer or another (e.g., "Do you meet deadlines?") and take about 20 minutes to complete. Bookmark the sites you find particularly helpful, so that you can return to them for future reference. Do a number of online tests and record your scores. Keeping a record of the test results may indicate that you favor opposite sides of your brain at different times.