What is the practical way to peel off zest of an orange?
The ideal tool depends on what you're trying to do with it.

If you want something nice and fine, which will release as much flavor as possible, avoid getting any of the pith, and not add distracting texture to a dish, use a fine rasp grater (sometimes known by the brand name microplane):



(There are also coarse rasp graters. That won't be any better than a standard grater. You want one that looks like the picture.)

If you want something small but visible, use a citrus zester:





You can get skinny little strips that tend to curl with the small holes at the end, and bigger curls like you've seen on the rims of cocktails with the wider hole in the middle. (Edit: added the second picture. That looks like it was fun.)

Finally, if you want big pieces to put in something to cook in something, then maybe fish out later, you can use a normal vegetable peeler: