Mustard is one of Europe's few native spices, although mustard also has been used in Chinese cooking for around 2,500 years as well.
Ancient Rome was quite the hotbed of mustard-making, and it is Rome that gives us our name for mustard: It is a contraction of mustum ardens, or "hot must," since the Romans often added crushed mustard seeds to unfermented crushed grapes. I've recreated a different Roman recipe for mustard that uses almonds, pine nuts, mustard seed, and red wine vinegar. The ferocious bite of this mustard—it should be made with black mustard seeds, the hottest variety—is mellowed by the richness of the nuts. It's a great accompaniment to roasted meats.

Holly A. Heyser
The basic idea behind making mustard is this: Grind seeds and add cool liquid. At its most basic, this is all mustard is. Both Chinese and English mustard (think Colman's) are nothing more than water and mustard powder. But there are some things you need to know to make great mustard.
First, you need cold liquid. What gives mustard its bite is a chemical inside the seeds reacting with cool or cold liquid. You also need to break the seeds to get at the fiery chemical—it's like cutting an onion. Heat damages this reaction, however, so to make a hot mustard use cold water, and warm water for a more mellow mustard. Mustard sauces lose punch when long-cooked, and should always have a little extra fresh mustard tossed in at the end of cooking.
This reaction is volatile, too. Left alone, your mustard will lose its bite in a few days, or in some cases even hours. But adding an acid, most often vinegar, stops and sets the reaction in place—this is precisely what happens with horseradish as well. Adding salt not only improves the flavor, but also helps preserve the mustard, too.
Once made, mustard is nearly invulnerable to deterioration. Mustard is one of the more powerful anti-microbial plants we know of, and, considering it is mixed with vinegar and salt, it becomes a heady mix no wee beastie can survive in. It is said that mustard will never go bad, although it can dry out.

Holly A. Heyser
You have three choices when it comes to which variety of mustard seed you use: white, brown, or black. White mustard undergoes a different, milder reaction than do brown or black mustards, which are far zingier. American yellow mustard is made with white mustard seed and turmeric, brown mustards are in most of your better mustards, and black mustard is used in hot mustards or in Indian cuisine.
Incidentally, the wild mustard all over California is black mustard. You can thank Father Junipero Serra for that one: He used mustard, which grows like a weed, to mark his travels in Alta California 250 years ago.
The famous Grey Poupon mustard—Dijon has been a center of mustard-making for nearly a millennium now—is traditionally made with stone-ground brown mustard and verjus, the tart juice of unripe grapes. I prefer this style of mustard, and most of my homemade mustards are grainy like Dijon. I grind my seeds with a spice grinder, but you could get all old-school and use a mortar and pestle.