The main things I check:
Set the camera to the fastest shutter speed, remove the lens, open the back, place your eye close to the shutter and press the button. You will get the very briefest glimpse of daylight, but with practice this can be enough to spot shutter capping.
Shutter capping happens when the second curtain catches up with the first, giving you either an unexposed portion of the frame or no exposure at all. It tends to happen at the faster speeds. If you can see light both sides (or the top and bottom) of the film window when the shutter fires then you're ok - I go by whether I can see the corners of the mirror box while looking closely at the left hand side, then the right. This is less common with electronically controlled shutters than it is with older models relying on spring tension. If the shutter is capping then it needs a CLA to sort that out.
If it passes that test then I set it to the slowest speed and fire it again. Usually this is a second, doing it a few times and comparing it to my watch's second hand will show how accurate it is. Again, more commonly a problem with the old clockwork shutters. One of my MXs had a very interesting idea of how long a second was but woke up after I wound and fired a few times. I already had an accurate MX so sat the two side by side on the table and compared the shutter sound at various speeds - the second body sounded identical so was obviously fine.