At its most basic, a compass is simply a magnetized needle that reacts to the Earth’s magnetic field and moves to indicate North. A simple compass like this can be used for rough direction finding and roughly taking bearings.
A small watchstrap compass like the one below is ideal for general orientation and keeping the map set to the North.
To work more accurately with bearings and to transfer these bearings to and from the map the compass is fitted onto a baseplate.
Over the years these have been tricked out with fancy features but the basics to look out for are the orienting lines and direction of travel arrow, a magnifier (very handy for small features or reading tight contour lines), Romer scales (very, very handy, making pinpointing grid references a breeze) and a measuring scale allowing easy distance measurement on maps.
Choose one that’s easy to read and operate – the time you’re most likely to need to rely on your compass is the time it’ll be most difficult to use it.
For more accuracy when taking bearings, some compasses are fitted with sights. For even more accuracy (how much do you need?) some sighting compasses are fitted with a mirror to ensure everything’s spot on when you read the bearing. This also doubles up as a handy shaving mirror which is nice.
This model also features an adjustable declination ring, allowing compensation for magnetic variation to be permanently adjusted using the wee screwdriver provided. Saves some faffing about but is not an essential feature (in my humble opinion!).
The main thing is to get something you’re comfortable with, learn how to use it, and practice when you can. The last place you want to be trying it out is a foggy hilltop!