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We present SQUEzE, a software package to classify quasar spectra and estimatetheir redshifts. SQUEzE is a random forest classifier operating on theparameters of candidate emission peaks identified in the spectra. We test theperformance of the algorithm using visually inspected data from BOSS as a truthtable. Only 4\% of the sample ($\sim$6,800 quasars and $\sim$11,520contaminants) is needed for converged training in recommended choices of theconfidence threshold ($0.2<p_{\rm min}<0.7$). For an operational mode whichbalances purity and completeness ($p_{\rm min}=0.28$) we recover a purity of$96.81\pm0.39\%$ ($99.30\pm0.14\%$ for quasars with $z \geq 2.1$) and acompleteness of $96.83\pm0.30\%$ ($98.42\pm0.15\%$ for quasars with $z \geq2.1$). SQUEzE can be used to obtain a $\approx$100\% pure sample of $z \geq2.1$. quasars (with $\approx$96\% completeness) by using a confidence thresholdof $p_{\rm min}=0.7$. The estimated redshift error is $1,500{\rm \thinspacekm/s}$ and we recommend that SQUEzE be used in conjunction with an additionalstep of redshift tuning to achieve maximum precision. We find that SQUEzEachieves the necessary performance to replace visual inspection in BOSS-likespectroscopic surveys of quasars with subsequent publications in this seriesexploring expectations for future surveys and alternative methods.  Keywords: cosmology: observations - quasar: emission lines - quasar:absorption lines

Spectroscopic QUasar Extractor and redshift (z) EstimatorSQUEzE I: Methodology