IR Spectra
Have a look at these two spectra. One if for cyclohexane (an alkane) and one is for cyclohexene (an alkene, with a C=C double bond).
The bottom IR spectrum is for cyclohexene. We know this because it has a peak at around 3100cm-1. This is absent in alkanes.
13C-NMR Spectra
Alkenes also have a characteristic peak when we look at the 13C-NMR spectrum. A peak between 115-145ppm is unique for alkenes. If it is absent, there are no C=C double bonds. If it is present, you can be very confident there is a C=C double bond in the structure.
Here is the spectrum for cyclohexene which shows the characteristic peak, shifted to 127ppm due to the C=C bond:
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