Once you get your head around precession, a gyrocompass is really a fairly simple device.
I found an article which had a very good explanation, and the figures are taken from that.http://www.maritime.org/fleetsub/elect/chap17.htm
Firstly, a gyro works by using a spinning disc of high rotational inertia, gained by having large mass towards the edge of a disc spinning at high RPM.
The first figure shows a free gyro, with three axis of freedom, two are on pivots while the third is the gyro wheel's spin axis. A free axis gyro will keep a directionally constant spin axis as there are no forces acting on it.
Precession is how a gyro resists the change in direction. When a torque is applied to a gyro, it applies a precession torque perpendicular. One of the more practical instances of this is countersteering on a motorcycle, as the rider aggressively twists the bars (by pushing on the inside bar), the front wheel generates a torque to lean the bike into the corner, allowing the motorcyclist to change direction very quickly.
The second figure shows the type of gyro I have made; a Pendulous Gyro. This is just a free gyro, but with a weight at the bottom. This weight applies a torque to ensure the spin axis is always horizontal. Because this torque is applied to a gyro, it in turn applies a precession torque, which rotates the gyro around its vertical axis.
The third figure shows how this is used to create a gyro compass. As the earth spins, the horizontal heading changes unless the gyro is pointing along the same spin axis as earth. The gyro attempts to follow the horizontal heading due to the torque from the pendulous weight. Once the gyro spin axis is aligned with the earth's spin axis there is no applied torque to the gyro, and its heading stabilizes.