How do we identify the molecular formula from the empirical formula of a completely unknown substance? Suppose you are given a sample of new (undiscovered) hydrocarbon with 600/7% $\ce{C}$ and 100/7% $\ce{H}$. (From combustion or any other method) We can find the empirical formula to be CH. Then how the we figure out whether it will be $\ce{C2H2}$ or $\ce{C4H4}$ or even something else?

Now we have identified the different compounds and can identify it through various reactions, but what would we do if we had something entirety new? How did chemists initially differentiate between these compounds?
If the empirical formula is known, then any method that will determine the molecular weight will do. Of merely historical interest is the use of freezing-point depression, nowadays, one would use mass spectrometry (electron-spray ionisation will leave most molecules intact).

This assumes that it is a reasonably small molecule, but only for those will the empirical formula be known before the molecular one.