First of all, remember there are two definitions of friction: static and dynamic, or sliding. The static friction coefficient is the ratio of the force needed to get an object moving from rest and the force pressing down on it. The dynamic friction coefficient is the ratio of the force needed to keep the object moving and the force pressing down. There are many ways to measure these coefficients of friction. A quick and simple way is to place an object on a plane surface and start raising the angle between the plane and the vertical. As you slowly increase the angle θ , all of a sudden the object will start moving. At that angle the sideways force is mg sin(θ). The normal force is mg cos(θ). The coefficient of friction, μ, is then the ratio: μ = tan(θ). That's it.
Now the measurement of the coefficient of sliding friction is a bit trickier. You have to increment the angle in small steps. At each step, give the object a little shove. If it stops, increase the angle just a little bit. Keep doing this until the object doesn't stop but keeps on sliding. Again the coefficient of sliding friction is μ = tan(θ). Look at http://en.wikipedia.org/wiki/Friction for a more detailed explanation.
(published on 05/01/2010)