  A comprehensive study of the measurement of star formation histories from
colour-magnitude diagrams (CMDs) is presented, with an emphasis on a variety of
subtle issues involved in the generation of model CMDs and maximum likelihood
solution. Among these are the need for a complete sampling of the synthetic
CMD, the use of of proper statistics for dealing with Poisson-distributed data
(and a demonstration of why chi-square must not be used), measuring full
uncertainties in all reported parameters, quantifying the goodness-of-fit, and
questions of binning the CMD and incorporating outside information. Several
example star formation history measurements are given. Two examples involve
synthetic data, in which the input and recovered parameters can be compared to
locate possible flaws in the methodology (none were apparent) and measure the
accuracy with which ages, metallicities, and star formation rates can be
recovered. Solutions of the histories of seven Galactic dwarf spheroidal
companions (Carina, Draco, Leo I, Leo II, Sagittarius, Sculptor, and Ursa
Minor) illustrate the ability to measure star formation histories given a
variety conditions -- numbers of stars, complexity of star formation history,
and amount of foreground contamination. Significant measurements of ancient >8
Gyr star formation are made in all seven galaxies. Sculptor, Draco, and Ursa
Minor appear entirely ancient, while the other systems show varying amounts of
younger stars.
