Theocides, this is a very good question. It is the most important question you can ask about magic: almost any spell that does not cause a physical effect is impossible to verify. Did it work? Did it not work? Was it coincidence? It's impossible to tell - except with statistical analysis or physical evidence.
There are four ways that I know of to obtain physical evidence. One, through statistics; if you attempt to influence the result of a coin toss fifty times, for instance, and obtain forty tails, then that is pretty good evidence. Two, through meditation; with enough of a certain type of meditation, it is said that one can mentally control a candle flame or move a small object. Three, through Hermeticism; certain Hermetic disciplines purport to enable one to mentally light a candle, for example, once one has a lot of experience working with the fire element. Four, evocation to physical manifestation; medieval grimoires state that spirits will appear to you, entirely visible and tangible, if you follow all of the directions faithfully.
Each of these approaches takes effort, some more than others. I have tried each over the past seven years. I am currently writing a book detailing the results of my attempts at all four; if you want to know what I found out, though, you'll have to buy my book. :-)
TheDarkSun, it is important to realize the difference between lack of evidence for existence, and lack of explanation. We may not be able to understand why headaches occur, but we can show that they do so. Magic is a different case, because both the mechanism and the existence are disputed.