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This paper is a self-contained introductory tutorial on the problem in proteomics known as peptide sequencing using tandem mass spectrometry. This tutorial deals specifically with de novo sequencing methods (as opposed to database search methods). We first give an introduction to peptide sequencing, its importance and history and some background on proteins. Next we show the relationship between a peptide and the final spectrum produced from a tandem mass spectrometer, together with a description of the various sources of complications that arise during the process of generating the mass spectrum. From there we model the computational problem of de novo peptide sequencing, which is basically the reverse problem of identifying the peptide which produced the spectrum. We then present several major approaches to solve it (including reviewing some of the current algorithms in each approach), and also discuss related problems and post-processing approaches.