IR Spectroscopy
The OH stretch of a carboxylic acid shows up from 3300-2500 as a characteristic wide, low band, sometimes with a small blip near the center. Another important for the carbonyl stretch of a carboxylic acid: an intense band from 1760-1690. The CO stretch appears in the region 1320-1210.
NMR Spectroscopy
Carboxylic acids exist as stable hydrogen-bonded dimers in dilute, non-polar solvents such as CDCl3. As such, the carboxylic acid proton shows up from 1013.2 ppm as a very broad singlet. (Sometimes it is so broad that it is not seen.)
Examples