How can you test for arteriosclerosis?

Depends where it is. Most tests aim to detect plaque causing obstruction to blood flow (e.g. Stress test to look for narrowing in coronary artery). However, atherosclerosis builds up slowly over time, and ideally should be detected before causes blockages. Doppler tests of carotid arteries or legs can image nonobstructive plaque in these locations noninvasively, and tell you if you're predisposed to this problem.
Image Artery Walls. It was long promoted (based on angiographic view & assumptions) that ds always produced narrowing despite lots of contradictory data. By the mid-1980s, with better analysis & checking evidence, it started to become apparent that plaque stimulated artery enlargements & narrowing was due to clots in the openings triggered by plaque rupture. Thus look at artery wall & wall thickness, not narrowing.