Scorpius X-1 was observed with the Japanese X-ray satellite Ginga on 1989 March 9-11 as part of a multiwavelength campaign. The source was observed to be on the flaring branch for the first 31 hr, on the lower normal branch for the next 7 hr, and on the flaring branch during a brief observation 17 hr after the final normal branch observation. We constructed a standard color-color, or Z-, diagram for Sco X-1. We then parameterized the state of Sco X-1 by determining s(Z), the distance along the Z-diagram from the flaring branch-normal branch vertex, as a function of time. Sco X-1 moved smoothly and continuously through the Z-diagram and was never observed to jump from one branch to another. All observed spectral characteristics (intensity, X-ray hardness ratios) are well correlated with s(Z), indicating that the source changes its physical state smoothly as it moves along the Z-diagram. The tight correlation of observables with s(Z) is consistent with variation of a single physical parameter being responsible for the changes in state. There is no correlation between s(Z), the rate of change of s(Z), and observed spectral characteristics indicating that there is little, if any, hysteresis or memory in the spectral state of Sco X-1 and that motion in the Z-diagram is essentially stochastic. The range of observed values of s(Z) depends on s(Z):s(Z) always changes slowly along the flaring branch when it is near the flaring branch-normal branch vertex, but can change rapidly during the excursions up and down the flaring branch which correspond to large flares. A self-similarity is observed in the temporal profile of flares which is independent of flare amplitude. The temporal characteristics observed-including quasi-periodic oscillations, high-frequency noise, and very low frequency noise-are consistent with previous observations of Sco X-1. Quasi-periodic oscillations are observed on both the normal branch (6.3 Hz mean frequency) and the lower flaring branch (14.4 Hz mean frequency), but not on the upper flaring branch. Limits are placed on the fractional rms variation of quasi-periodic oscillations on the upper flaring branch of less than or similar 2% of the total intensity. The characteristics of the observed red noise components are found to vary along the flaring branch. The fractional rms variation of very low frequency noise increases from less than or similar 2% to greater than or similar to 6% as Sco X-1 moves from the flaring branch-normal branch vertex to the upper end of the flaring branch; the power-law index for very low frequency noise, alpha, remains constant along the flaring branch (alpha = 1.72 +/- 0.01). Both the rms fractional variation and the width of the high-frequency noise component vary as Sco X-1 moves out the flaring branch, with the rms fractional variation decreasing from approximately 3% to less than or similar 1% and the Gaussian rms width decreasing from approximately 15 Hz to approximately 5 Hz. No dependence on s(Z) is observed for any of the temporal characteristics. A search for coherent pulsations was made in both high time resolution optical and X-ray data. Limits on the 95% confidence limit pulsed amplitude are set at 0.10% (optical) and 0.19% (X-ray) for nu < 50 Hz and 0.26% (X-ray) for nu < 400 Hz. A search was made for optical quasi-periodic oscillations in data obtained while normal branch oscillations were observed in the Ginga data; none were seen with an upper limit to the fractional rms variation of 0.23% of the total intensity.