The size can be calculated from structure. Many organic compounds are flexible and not spherical so the diameter should be carefully defined.
For my practical task (diffusion in nanopores) I have found suitable definition from catalysis : hydrodynamic diameter is diameter of least cylinder where molecule could be placed.
For diffussion in homogenious media, hydrodynamic radius ~ is square root from a2+b2+c2, where a, b and c are distance from center of molecule in XYZ.
However, molecules are not absolutely rigid so slow diffusion is possible in pores that are smaller on 1Å of calculated size. For "comfortable", high-speed diffusion, the size of pores should be 1.5-2 times larger than hydrodynamic diameter of molecule.
If we consider small molecules, X-ray can be used to determine the size of a molecule in a crystalline sample.
For large molecules, for example polymers, various types of size-exclusion chromatography (SEC) exist, coupled with some sort of a detector to measure the average molecule size, although I am not exactly sure what method is usually used for molecule size measurement after SEC.
Really large molecules like DNA can even be visualized with proper equipment, but this is hardly a routine procedure.
Use computational methods. For higher accuracy there is atomic force microscopy but it is not a routine technique. You have to define the type of the molecule and chose the technique. What works for one class may not work for other.