We present a compact laboratory system for near edge soft X-ray fine structure (NEXAFS) spectroscopy that was developed using a laser-plasma light source. The source is based on a double stream gas puff target. The plasma is formed by the interaction of a laser beam with the double stream gas puff target approach. The laser plasma source was optimized for efficient soft X-ray emission from a krypton/helium target in the range of 1.5 to 5 nm wavelength. This emission is used to acquire simultaneously the emission and absorption spectra of soft X-ray light from the source and from the investigated sample using a grazing incidence spectrometer. The measurements in the transmission mode reveal the features near the carbon K-α absorption edge of thin PET film. From those features, the composition of the sample was successfully obtained. The data are in agreement with synchrotron measurements. In the paper, the detailed information about the source, its optimization, the system, spectral measurements and the results are presented and discussed.