I was watching CSI last night and their lab guys are just fantastic. “Hey, Dude, what’s this blue powder”. Quicker than a commercial break, they say it’s silica, talc, (& something else I can’t remember) and in that combination, it’s pool chalk.
(Me, I looked at the blue powdery stuff, and said to my wife that it was pool chalk. I’m sending my resume to the FBI today.)
There are lots of methods, including microanalysis and Xps that will give the elemental composition (e.g. % carbon iron etc).
The solubility will be checked - any soluble material is fairly easy to analyse by a number of methods (UV, NMR)
Mass spectra will look for any small molecules and often tell you what their formula is
X-ray crystallography will determine the structure of any crystalline parts
IR spectroscopy is useful on the insoluble portions.
sorry for all the acronyms
by putting all the pieces together a good idea of the identity of the unknown substance can be put together. Unless it is completely exotic which is unlikely then given enough sample (say .1-10 gr) the structure should be determined in a week or two. Even quicker if resembles something known.