Sometimes knowing where you are is less important than enjoying where you aren't, like at work, in traffic, or looking at your wallpaper. That said, once off the pavement you should always know where you are, at least within reason. With modern technology it seems very easy to tap a few buttons and...unless the battery is dead, or the thing got dropped, or who-knows-what. If you have a map, a compass, and can identify three landmarks, you can always figure out where you are.
Maps have become fairly standardized thanks to the United States Geological Survey, or USGS, so there isn't much to discuss there. When choosing your compass, more options exist, but like most gear decisions, the real questions are: how are you going to use this, how often, and how important is it? If you are picking up a map and compass as a backup to your smartphone, make sure the markings are easy to read and you know which end is which. For navigating in the backcountry, being off by two degrees might mean missing the water source by 300 meters.
The most basic way to find the north/south axis of the Earth is to float a magnet in liquid or air. If it has ends, the magnet will always align itself. If the North end is marked, you have a compass. With a little shopping, you can find almost anything with a cheap compass stuck to it, from whistles to pens to cufflinks. Few of these have been built to be of much use, but that doesn't mean a small or inexpensive compass isn't a good one.
Key factors to look for in a compass:
Fluid filled with oil or alcohol that are less affected by air temperature and pressure and provide damping so the needle moves smoothly.
Brass fittings that will not affect readings and establish a boundary to keep ferrous materials at a safe distance.
Degree markings that allow you to translate what you know from the compass to the map and back again.
All of these can be found in an 'eyeball' style compass that pins to your shirt or pack strap and provides a quick reference, but it won't be too helpful when plotting a course or triangulating your position. To provide the most utility, a compass needs to be able to record a bearing or heading and allow the user to translate that information.
To clarify some concepts, we'll take a very short course in Orienteering, the craft of navigating by map and compass:
North, South, East, and West are always basically the same no matter where you are on the planet. When giving directions, this is very handy because everyone agrees on those four points. To be more precise in describing where something is and how to get there, we use degrees to describe the directions between N, S, E, and W.
Knowing that north is 0 degrees, east is 90, south is 180, and west 270, you can figure out that 160 degrees is closer to south than east, but more importantly, 160 degrees is always exactly the same for everyone. If two people start from the same point and travel 100 meters following the bearing 160 degrees, they stop at the same spot. Using the same system, if I gave you three sets of bearings and distances to find a treasure and you follow them precisely, you find the loot.
If any bearing or distance is not accurate, however, you might get 'close enough' or miss everything completely.
To be accurate in navigating, you must take precise sightings and bearings. Sighting is the process of lining up the direction of travel arrow on the compass with a landmark or feature you can see and determining its bearing from your position by turning the dial until the north marking and arrow are aligned. The finer the markings on your compass and the less you must move your eye and the compass to take a sighting, the more accurate you will be. A bearing is determined on your map by drawing a straight line from your current position to your destination. A baseplate style compass is essential for this since it allows you to orient the map with the compass and see your line precisely.
So, how much compass do you need? The housing, fluid, and needle are about the same in a $12 starter model and the $100 international. The important features will increase accuracy in reading, notably the detail level of the dial and a sighting mechanism. A classic 'military' or lensatic sighting design uses an arm holding a lens and a sight wire that are aligned with the dial. The more modern and popular sighting style uses a mirror that is postioned over the dial so the object and compass can be seen in the same field of view. The mirror also acts as a cover to protect the dial from damage and serves as a daytime signalling device. Further enhancements in better compasses will include an adjustment for declination, additional scales and tools on the baseplate, and overall build quality.
Experience may convince you that the good stuff is worth it, and a navigator with an accurate map and precision compass will outperform a GPS unit in speed and reliability every time, but if you're just following blazes or the 'trail' is an old road, something that just reminds you which way is North will get you back to the car safely.
Needle: Indicates North and South, usually with red (N) and white (S) ends
Housing: round enclosure conatining the needle and damping fluid
Dial: Ring around the face of the housing holding the needle marked with the cardinal points (North, South, East, West) and degrees.
Direction of travel arrow: Line scribed on the baseplate and used to record bearings on the map or headings while taking readings from the field.
Baseplate: flat rectangular clear plastic that the housing is attached to
Bearing: The direction you want to be going.
Heading: The direction you are actually going.
Declination: The specific difference between True North and Magnetic North. Will be indicated on all topographic maps.