How is coefficient of friction calculated? How is coefficient of static friction and coefficient of kinetic friction is calculated in real life without knowing the frictional force?
 A: Static coefficient
I simple experiment would consist of taking a ramp of material $A$ and a block of material $B$. Let the ramp start completely horizontal and start lifting the ramp gradually. As soon as the the block starts sliding, register the angle of the ramp with respect to the ground, $\theta$. Then a simple analysis of forces should do the trick.
$$\begin{align}
m_B\, g \sin\theta &= \mu_{st}\, m_B\, g \cos\theta\\[6pt]
\Longrightarrow \mu_{st} &= \tan\theta
\end{align}$$
This would be the static friction coefficient of material B against A.
Kinetic coefficient
For this you will need a dynamical situation, again take your two materials of choice and using a track made of material $A$ you can shoot a block of material $B$ along the track. If you know the initial speed, $v$, you know its kinetic energy, by choosing either a long track or a small enough speed, you can determine how much energy is lost by friction by measuring the distance travelled, $D$.
$$ E_{kin} = \mu_{kin} m_B\, g D$$
therefore you get
$$\mu_{kin} = \frac{v^2}{2gD}$$
A: I can not give you an example for all surfaces, but for an inclined plane, the formula is pretty straightforward. Suppose you wanted to find the coefficient of friction between a block and an incline. Keep the block on the incline, and if the block is stationary, try to increase the angle of incline until the block just begins to slide. At this point, the force on the object is just equal to the maximum value of static friction, i.e. $\mu\ mg\ \text{cos}\ \theta$ where $\theta$ is the angle of incline. And what is the force on the object? Well, it's the other component of weight i.e. $mg\ \text{sin}\ \theta$.

For equilibrium condition, you equate these two-$$\mu\ mg\ \text{cos}\ \theta=mg\ \text{sin}\ \theta$$
from which you simply get- $$\mu=\text{tan}\ \theta$$
For an increased accuracy, repeat the above experiment with heavier/lighter blocks, different inclines of the same material, and also take care to keep the surface smooth enough to allow a uniform incline. Take the mean and you will get a really close value.  Note that in this answer I have simply shown a really general method which is far from rigorous, but I hope this still helps
A: First, I think the term 'dynamic friction coefficient' is more widely accepted than the term 'kinematic friction coefficient', which I am assuming refers to the same concept.
In any case, judging from my quick bibliographical search, there are no widely used methods available. There is no shortage of proposals though. Check up, for example:
Determining dynamic friction using a modified Kolsky method
or
Dynamic friction measurements at sliding velocities representative of high-speed machining processes
and in the context of an industry in which I have actually worked (and no, there was no standard method to speak of),
Dynamic friction coefficient measurement of granular fertilizer particles
And also patents:
Dynamic friction coefficient measuring apparatus
