Probably the main thing to understand about effects order is that an effect modifies the sound it receives. This means if you plug your guitar into a fuzz box, the fuzz box gives you a fuzzy guitar sound - pretty obvious, huh? If you then plug the fuzz output into a wah pedal input, then the wah works on the fuzz sound, giving you a synth-like wah sound.
If you plug first into the wah, then into the fuzz, it gives a completely different sound. That's because the fuzz is working on a guitar sound that already has a wah effect. You may know that distortion effects like fuzz have more effect on loud sounds than quiet ones (that's why they sound cleaner when you roll off the guitar volume). And a wah pedal makes different notes and frequencies louder and softer as you rock the pedal, so rocking the pedal also now controls the amount of fuzz as well, giving what most players prefer as a more interesting effect.
There are no rules on effects order. You won't break any pedals by putting them in a 'wrong' order. In fact, experimenting is the best way to learn, and in doing so, you can come up with many unusual and interesting sounds. There is, however, a typical order of effects that I've listed below.
Before we get into the order, though, you might like to consider why, when & how you use effects. My most deep piece of wisdom to pass on is that the subtle use of effects is suitable for long periods of use, while intense effects have most impact when used briefly.
For example, light phasing or chorus can be used for an entire song, adding some texture to backing rhythm. Dramatic effects like strong delay, wah, or even playing techniques such as continuous fast picking without a rest, become tiresome when overused.
I think the most special effects are those that you can only just detect are turned on. In the late 70's, I had many people trying to figure out how I got a such a special overdrive sound for my solos. All I did was to use a faulty (weak-sounding) phaser set to a slow speed before the overdrive, to give just a hint of movement. You can use understated effects easily to craft your own signature sounds.