"What is the method to measure entropy and enthalpy"?

Answer 1

Ussualy, entropy and enthalpy are not directly measured. Even though, you are able to calculate it from other termodynamic parameters you can determine.
If you take a look into a termodynamics course, you will understand better the conection between some parameters of an termodynamic system you can measure(e.g. temperature, pressure) and entropy and enthalpy.

Answer 2

Steam calorimeters are used to measure steam quality (amount of moisture which can vary) which then locates a point on a steam chart (or steam table by interpolation) that identifies the enthalpy and entropy of the steam header sample.

Answer 3

if you're talking about entropy in the information theory it is measured based on the probabilities of occurency of all the possible symbols of the alphabet of the information source.
For example, if there is a binary source of information, that is, its alphabet is {0,1} the entropy of this source of information is:
P0*log(P0)+P1*log(P1)
where P0 is the probablity that the symbol transmitted by the source is a 0 and P1 is the probability that the symbol transmitted by the source is 1.
Usually since this theory is used in digital communications, to calculate this you use logarithm in base 2, that is ln(x)/ln(2)

Answer 4

something called a bomb calorimeter is used to measure enthalpy. i don't know how entropy is measured.