Stage 2: Extracting the spectra

Extract the +ve and -ve images of the spectrum seperately. You can use optimal extraction if you like, and if you used the same nod distance for the standard star, you can use the standard star observations to generate the profiles with which to optimally extract the target spectra. After you extract the -ve spectrum, multiply it by -1 to make is positive. Keep the profiles that you use around for later use.

Check for a shift between the specta. This needs to be done on something bright; I suggest doing it only on the standard star spectra, however if your target is brighter than your standard (you might have been doing monitoring, or looking for weak lines on a strong continuum etc), then you could do it to the object spectra too.

Basically, cross-correlate the main-beam and offset-beam spectra. If you get a shift of more that say 0.2 pixels, shift the offset beam spectrum to match the main-beam spectrum. If you're only measuring this from the standard star spectra, apply the same shift to the offset spectrum from the target data too.

Add the main and offset beam spectra together. This forms the "observed spectrum" of each object (be it the standard star or your target).

It'll probably keep things simple if you normalise each spectrum by its exposure time at this point.