There are quite a few you can do with just your ears and some others that require a minimum of audio gear. I'll list some tests you can do, a simple explanation of what that test can show you and then a link to a longer explanation of how to do the test and how to interpret it. The best way to do the tests is simultaneously as a comparison in performance between several systems. It is easy to forget what a given system sounds like if there is a day or so between tests. Sometimes the differences are so dramatic you could remember them years later though.