The simplest way to zest citrus is to use a tool called a citrus zester. This tool has very small holes at its top that will cut very shallow ribbons out of the citrus fruit. Both a vegetable peeler and a box grater are tools that can be used to zest, however, a citrus zester will yield the best possible result.
For finer shreds, use a microplane grater.
Depending on the particular shape of zest desired, the zester will be used in different ways. If the zest, will be chopped, then rough zesting can be done in any fashion. However, if the zest needs to maintain a specific shape for a garnish (or any other reason), long steady strokes from one side of the citrus are necessary. Steady strokes will create long noodle-like strands, which are great to use as garnish. One note of caution: citrus zest has a very dominant flavor so it is a good idea to blanch and shock the zest previous to garnishing.
If a citrus zester is not on hand, a vegetable or box grater will work acceptably well. However, the vegetable peeler is a coarse zesting tool and a great deal of bitter tasting pith may be scraped off along with the desired zest. When using a vegetable peeler, do not press hard into the citrus to avoid removing any pith. Using a box grater is probably the quickest way to zest, but it is also the most wasteful and sloppy. When using a box grater to zest, hold the citrus firmly in one hand and grate the zest off as you would grate cheese. The grating motion will cause a large amount of juice to be forced out of the zest, lessening the zest's aromatic taste.