That's the general idea, yeah. I always start with the power supply because that part is under the most electrical strain, and tends to get hot. That means its components are often both the first to fail, and the most likely to cause weird problems when they do fail. Other than that, it's just intuition about how I think the device probably works, and a lot of trial and error. Major bonus points if there's a datasheet available, or a kind forum poster has had a similar problem to give me a lead on where to look.