The laser, detection system, and methods that enable femtosecond broadband stimulated Raman spectroscopy (FSRS) are presented in detail. FSRS is a unique tool for obtaining high time resolution (<100 fs) vibrational spectra with an instrument response limited frequency resolution of <10 cm(-1). A titanium:Sapphire-based laser system produces the three different pulses needed for FSRS: (1) A femtosecond visible actinic pump that initiates the photochemistry, (2) a narrow bandwidth picosecond Raman pump that provides the energy reservoir for amplification of the probe, and (3) a femtosecond continuum probe that is amplified at Raman resonances shifted from the Raman pump. The dependence of the stimulated Raman signal on experimental parameters is explored, demonstrating the expected exponential increase in Raman intensity with concentration, pathlength, and Raman pump power. Raman spectra collected under different electronic resonance conditions using highly fluorescent samples highlight the fluorescence rejection capabilities of FSRS. Data are also presented illustrating our ability: (i) To obtain spectra when there is a large transient absorption change by using a shifted excitation difference technique and (ii) to obtain high time resolution vibrational spectra of transient electronic states.