When you say you're given the peaks I assume you mean the frequency or wavelength of each peak. Then you get a book that gives the peaks by element. Peaks for elements different in number, intensity, etc but generally there are 2-5 strong "lines"(peaks) in the spectrum that will show up when only small quantities of an element are present. USUALLY lines have been picked out for each element that don't have major interferences from other elements. Then you systematically go through the periodic table and "read" the elements one by one. It complicates things when major quantities of several elements are present because even the weak lines show up then. I always diluted my sample and made another spectrum and that weeds out a lot of confusing clutter. Finally, a tip. Ignore lines for Cl2, I2, Br2, H2, N2, O2, S, and a few other elements; they don't have definitive lines in the region where you usually look not to mention that most are gases. There are more usable peaks in the uv region (2500A - 3800 A) than other regions although the visible part of the spectrum, especially in the 4000A to 7,000 A region, is best for K, and a few other elements. (Na for example has a doublet in the visible(at 5890.0A and 5895.9A) BUT also an almost as strong doublet at 3302.3A and 3303.0 A in the UV so you don't need visible to find Na. The uv line for K often has too much interference). I have waxed enthusiastically but I don't know if I've answered your question or not. I never had the luxury of having peak wavelengths laid out for me; I had a photographic film with a calibration using Fe. I also had a blowup of the complete Fe spectrum with those "strong lines" I talked about above inked in on the blowup and by following the road map I could check for 40-50 elements in a matter of a minute or two.
