Modern wristwatches are rather miraculous. For the price of a good dinner, you can buy a timepiece potentially accurate to a few seconds a month, with a self-contained power source, and with a lifetime of decades.
The trouble is, no one gives them respect. They're now jellybean consumer electronics that people simply buy and forget. But with a little work, you can bring your watch up to its true potential; what's more, you'll always have the right time, you'll know it's the right time, and you'll know where to get even more accurate time if you need it.
All clocks have two parts: an oscillator and a counter. The oscillator provides a stable, cyclic event, like the once-per-second beat of a pendulum or the regular vibrations of a tuning fork. The counter counts the events and displays the current count, formatted in the usual year/day/hour/minute/second way.
The best overall current technology for wristwatches uses:
The quartz crystal is just a chunk of rock. If you hit it, it vibrates, just like anything else. Crystalline quartz, though, will induce charge on its surface as it vibrates, so that makes a convenient interface to electronics---with suitable feedback, an electronic circuit can cause the quartz to continuously hum at a frequency determined by how large the crystal is.
For most watches, the crystal is a few millimeters long, and it vibrates at 32.768 kHz (that is, 32,768 times per second). The number has to do with convenience: if you successively divide the number by 2, easy with digital circuits, you find that fifteen such stages give you a once-per-second digital signal.
The manufacturer has carefully cut the crystal in your watch not only to the right frequency, but in a way to keep the drifts with temperature very small by using x-ray diffraction to orient the slice with respect to the crystal's crystallographic axes. (In the world of high precision, temperature is one of the big concerns, along with pressure, ambient magnetic fields, vibration, and quality of vacuum, depending on what it is you're doing.) The crystal is then sealed in a small metal can, so that no contaminants can affect its frequency.
So, let's start with setting your watch to the right time. There's a Yogi Berra-ism I like:
Where does time come from? It comes, ultimately, from a place called the International Bureau of Weights and Measures, headquartered near Paris. (It does not come from the Earth's rotation, or from the Earth's orbit about the Sun. These either vary too much or are not readable to high enough precision. Modern time is a man-made artifact.)
The Bureau coordinates an internetwork of clocks maintained by many labs around the world; there is an algorithm that performs a sophisticated average of the clock comparison reports as they come in, to generate coordinated universal time, or UTC, the world scientific timescale. It is sometimes called a "paper clock", since no actual clock generates UTC directly---only on paper does UTC emerge. Of course, if you have timestamps referred to actual radio clocks like UTC(NIST) or UTC(GPS), you can convert to true UTC once the corrections have been published.
The U.S. Naval Observatory disseminates the official time in the US. USNO maintains a network containing some 60 cesium atomic clocks (which contribute about one-fifth of the BIPM's clock network mentioned above), as well as several hydrogen masers. The National Institute of Standards and Technology's Time and Frequency Division is also involved with time and frequency research, including the development of advanced trapped-ion clocks.
So how do you use these clocks? Easy, usually. NIST in Colorado broadcasts shortwave radio signals with clicks and beeps and a voice announcement on the minute. Here's a list of useful stations in North America. (If you're not in North America, listen to the WWV frequencies anyway: they're the standard time-service frequencies.)
One of these usually has an audible signal; just tune your radio to the various frequencies and pick the best one. They're AM signals, like most shortwave broadcasts.
On the half-hour, WWV has a longer explanatory message. (I've heard that the definition of a radio addict is someone who can recite the WWV message from memory.) By the way, the time it takes for the WWV signal to get to you from Colorado is only a few milliseconds; the error won't affect anything unless you have superhuman reflexes.
If you don't have a radio that can receive WWV or CHU, you can get pretty good time from the Internet using NTP, the Network Time Protocol. See the NTP homepage for instructions on how to run NTP on your computer; I'd recommend starting with ntpdate, since that program will set your computer's clock once, then exit (the more elaborate NTP client will run forever, tweaking the local clock every 20 minutes or so).
OK, you've set your watch to WWV. You should try to make the radio click coincide exactly with the changing digits on the watch; this will give you accuracy of 0.1 second or so.
Of course, it won't stay set, and the whole point here is that you can tweak the watch's innards to minimize the rate at which it will drift.
You'll need a small screwdriver; if you have the jeweler's or eyeglass types, those are fine. When you open the watch, keep careful track of the various screws and plastic spacers. (Mine also has an O-ring for sealing.) Your target is something called a trimmer capacitor, a circular ceramic object that has a screwdriver slot in the top. Turning the trimmer will adjust the rate of the watch, to perhaps plus or minus 30 seconds per month at the limits.
For now, just make a careful note of the current position of the trimmer with respect to the other parts of the watch. The first step is to measure the error of the watch; then the trimmer will be adjusted to take out the error.
Keep a sheet of paper with times, notes, and sketches. You'll find it helpful as a record and for when you make adjustments.
It's a bit difficult to estimate tenths of seconds---one trick I use is that if the click falls right in the middle of the digit changes, I know it's a half-second. Musicians, especially percussion types, will have the edge here.
It's a matter of degree, of course. Everyone needs time good to a few minutes, to meet people, schedule things, and so forth; but other applications, used by everyone in modern society, depend on very precise time in a much more subtle way. Airline travel and the telephone network, for example, are just the tip of the iceberg.
Navigation was, and still is, the canonical application for precision time. In the mid-18th century a fabulous prize was offered by the British government for a solution to the problem of longitudes. (Ships can determine latitude just by watching the pole star, but longitude needs a time reference. There were purely astronomical schemes involving lunar parallax or occultations of Jupiter's moons, but these were impractical aboard ship---an extremely accurate mechanical clock was needed.) The prize, 20,000 pounds sterling, an incredible fortune at the time, was won by John Harrison, a British clockmaker. (An engaging account of this saga, Longitude, complete with hero and villain, was recently written by Dava Sobel.)
Today navigation is done by radio, and the pinnacle of modern navigation is a system called GPS (Global Positioning System). It is a network of some twenty-four satellites in high orbit; each contains an atomic clock (the cesium kind) and a radio transmitter. The user, somewhere on or above the Earth, holds a little cellular-phone-like box. The box records the time it took the radio signal to travel from each satellite; there are always at least four satellites visible overhead. This is enough information to do a "triangulation" (but in three dimensions) to compute the user's position (and to tell him the correct time). Ordinary "pseudorange GPS" is accurate to a few tens of meters; "differential GPS", which relies on broadcast corrections, can get down to one-meter accuracy, and "kinematic GPS" or "carrier-phase GPS" can get down to millimeter accuracy, if you're willing to take data for a few hours and you have a set of accurate satellite orbital elements.
Carrier-phase GPS is so accurate, in fact, that one cannot express GPS coordinates in terms of ordinary latitude and longitude, because GPS is more precise than the definition of latitude and longitude. New definitions are needed, and these must take into account a planetary surface that's far from being a solid shell of rock. With GPS, one can see continents moving and earthquake faults sliding, because these phenomena involve motions of a few centimeters per year, which is easily visible from the GPS measurements. This means your coordinates are constantly changing, even if you staple yourself to a mountain.
Time is the most accurately realized fundamental unit. In fact, since 1983 the meter no longer exists---it is now defined as a certain fraction of a second, namely 1/299,792,458 of a second (or, more verbosely, the distance light travels in that fraction of a second; but relativity tells us that space and time should measured in the same unit, namely the second.) (And what is a second? Since 1972, the definition has been 9,192,631,770 ticks of a cesium clock.)
Time drives many bleeding-edge investigations in physics because it's the sharpest tool available. Some people think that accuracies of a part in 10^18 (one nanosecond per 30 years) are achievable in the near future. With such clocks, one could do, for example, desktop experimental general relativity.