What are some general tests that would determine an unknown compound? I know a little bit about unknown compounds but I am still new to the topic here. I know that you could use filtration, chromatography and distillation. You can also combine the unknown with others to form a compound. And you can measure properties and such and such to figure out what the compound is.

If I were to do this, what should I watch out for, and what would be the best way to proceed? I would appreciate it if you don't go "PhD" on me. 

This question will be ambiguous for most people, but I am looking for a general idea and what you would normally do, instead of "what I would do in this situation".
As usual, it depends on what is available. 

Mass spectrometry, $^{1}\ce{H}$ and $^{13}\ce{C}$ NMR, IR, UV/VIS spectroscopy, would be obvious choices in organic chemistry nowadays. XRD of a suitable crystal would be nice to have! 

Back in the days, (undergrad) laboratories didn't have sophisticated analytical instruments and you were happy to find a melting point apparatus, a refractometer and an IR spectrometer.

You would have used IR spectroscopy to identify funcional groups, possibly supported your hypothesis by using staining reagents for TLC, like Dragendorff's reagent and then started to synthesize derivatives from which you knew that they show sharp, well-defined melting points. 

You would have converted  


amines to sulfonamides
carbohydrates to osazones  
ketones and aldehydes to 2,4-dinitrophenylhydrazones or semicarbazones


and compared the melting points of the derivatives with tabulated values. Those were the days&hellip;