Read chapters 6-7 in Lerdahl and Jackendoff's GTTM. See also pp. 68-69 in the IAT materials for suggestions of what to focus on. Key concepts are 1) time spans (TSs) are hierarchic, 2) TSs rely on grouping and metric analysis, 3) every TS has a head (meaning most important event in the TS), which may occur as any event within TSs according to rules, and 4) that cadences (except for the half cadence) comprise two chords, the cadence chord itself and the "penult," the V chord prior to the cadence, which is subordinate to the cadence chord. Keep in mind that TS reduction is a bottom up approach (from the smaller to the larger TSs, that is, from surface events to higher level events. The primary notation for TSR is the tree diagram; music notation is considered "secondary" notation.
Read chapters 8-9 in GTTM. See also pp. 69-70 in the IAT materials. A key concept is that while TSR relies on most important events within TSs, prolongation reduction relies on tension and relaxation. It comes closer to, but is not the same as, Schenkerian reduction. TSR is a preliminary stage in PR and is a top down approach to understanding tonal relationships. Tree diagrams are the primary notation, and musical notation is again secondary. In general, musical notation is less helpful in PR than in TSR.