There are and have been many appraoches,

such as:

- Comparison of the spectra of different materials, which are different in structure, but share only one group. Whatever is the same in each spectrum, belongs likely to the strucutre present in each sample.

- Comparison with other techniques, such as Raman spectroscopy, maybe neutron scattering (Atleast for phonons in crystals this yields results)

- Comparison with theoretical predictions (e.g. nowadays by DFT or even semi-empirical calculations by hand in the early days). There are whole books with tables of calculated/estimated frequencies of molecular groups.

- Polarisation/Symmetry behavior of specific - although this more applies to crystals/samples with defined orientations.

EDIT:

- using isotope effects. If you, for example switch out hydrigon with deuterium in your molecules, each molecular vibrations involving the hydrogen groups, will be at lower frequency. This is possible for many materials.

- Comparing spectra of materials, where certain atoms are switched with atoms from a different period of the period table. For example, having a molecule, where you can switch C for Si, but which otherwise have the same structure, and compare those spectra you will see, what is mostly impacted by that.

And then it is a puzzle to solve. Making experiments/hypothesis and testing until a stable picture emerges.

Best,

Michael

You can find some information on early applications of IR spectroscopy (and further references) in the paper of Barnes and Bonner

Scanning a pure material of an object.