How do you calculate the force of sliding friction?

That really depends on what you know about the situation. The simplest way is if you know the weight of the object and the materials you could use:

##F_F## ##=mu F_N##

Where you look-up the coefficient of sliding friction (##mu##). This assumes you're sliding along a horizontal surface so that the normal force is equal and opposite to the weight of the object. If your surface is not horizontal, you'll have to use trig to calculate the magnitude of the normal force first.

An experimental way do determine this would be to slide the object at a constant speed and measure the force applied to it. If the velocity was constant, there is no and according to Newton's 2nd Law, the force applied must be equal to the force of sliding friction acting against the motion.

This can be done by attaching a spring scale to the object and reading the scale while pulling the object at constant speed across a horizontal surface.

See also this answer:http://socratic.org/questions/how-do-you-calculate-coefficient-of-friction