Mostly spectroscopic techniques are employed for this purpose. We can also use meteorites to study other planets but unfortunately we do not have access to meteorites came from each and every planet. Here on earth you can study meteorites using different analytical techniques such as XRF, XRD, SEM, SIMS etc. and these are non destructive methods. Also there are few destructive techniques including ICP, AAS, TIMS etc.
It largely depends on the facilities available at your work place. The more sophisticated and advanced instruments you have, the accurate would be your results. I agree with previous answer by Arshad Ali.
apart from the methods mentioned above, one can perform microwave spectroscopy, which directly detects the microwaves emitted from celestial bodies, and based on standards, one can identify chemicals present on the same.