What exactly are you looking for? Elemental Composition? Molecular structure?
Most of the time, chemists use combination of several analytical apparatus to identify a molecule. That is, mass spectroscopy, elemental analysis, nuclear magnetic resonance, infrared spectroscopy, etc. Mass spectroscopy gives information on the weight of the molecule as well as weight of its unstable fragments. Elemental analysis gives information on the weight percentage of several element, primarily carbon, hydrogen, and nitrogen (some other elements are also available). Nuclear magnetic resonance gives information on ratio of number of hydrogen as well as its surrounding environment (this can be expanded to other NMR active elements too). Infrared spectroscopy gives information on the vibrating groups in a molecule. C=C stretching modes, -CH3 rotating modes, etc.
The most realistic apparatus to make is elemental analysis. However, even this isn't so easy since you need very high sensitivity scales, good catalysts so that the sample burns completely, etc.