How would I go about finding the resonant frequency of a glass pane?

IMO, your expectation that every object has a single resonant frequency might be misguided. There is an old alarm bell in my parent's house that sounds one clear note if you tap it in a certain place, it sounds another, slightly different note if you tap it in a certain other place, and it sounds a discordant combination of the two if you tap it in any other place.

I'm going to assume that when you say "vibration," you are talking about mechanical vibrations. Every physical object that can vibrate will do so in any number of distinct vibrational modes, and each mode has it's own frequency. Those modes typically will come in "familes" whose members all resonate at frequencies that are related to one another by rational numbers. (e.g., see https://en.wikipedia.org/wiki/Harmonic_series_(music)).

Glass is a good material from which to make bells (assuming an application in which nobody's going to whack it hard enough to break it.) If your window pane doesn't ring when you tap it, that's probably because whatever structure is supporting it is damping (i.e., sucking the energy out of) most or all of its vibrational modes. The key to letting a bell ring out loud is to contrive some kind of a support structure that only touches it along the nodes of some desirable set of vibrational modes.

Also, what sound it makes will depend on which modes you excite when you tap it. That will depend on exactly where you tap it, and probably on physical qualities (e.g., the hardness and size) of the tapper.

the resonant modes of big sheet of glass will be in the low frequency range, 100Hz and lower. A rectangular sheet will exhibit a spread of different modes because a range of different wavelengths can be fit onto it. Predicting mode shapes is a complicated business but running experiments to find the actual mode shapes is not hard, as pointed out by @Pieter in his comment. I can explain methods which do not rely on digital equipment and software if you are interested.