This is the first in a series of papers examining the demographics of star-forming galaxies at $0.2<z<2.5$ in CANDELS. We study 9,100 galaxies from GOODS-S and UDS having published values of redshifts, masses, star-formation rates (SFRs), and dust attenuation ($A_V$) derived from UV-optical SED fitting. In agreement with previous works, we find that the $UVJ$ colors of a galaxy are closely correlated with its specific star-formation rate (SSFR) and $A_V$. We define rotated $UVJ$ coordinate axes, termed $S_mathrm{SED}$ and $C_mathrm{SED}$, that are parallel and perpendicular to the star-forming sequence and derive a quantitative calibration that predicts SSFR from $C_mathrm{SED}$ with an accuracy of ~0.2 dex. SFRs from UV-optical fitting and from UV+IR values based on Spitzer/MIPS 24 $mumathrm{m}$ agree well overall, but systematic differences of order 0.2 dex exist at high and low redshifts. A novel plotting scheme conveys the evolution of multiple galaxy properties simultaneously, and dust growth, as well as star-formation decline and quenching, exhibit mass-accelerated evolution (downsizing). A population of transition galaxies below the star-forming main sequence is identified. These objects are located between star-forming and quiescent galaxies in $UVJ$ space and have lower $A_V$ and smaller radii than galaxies on the main sequence. Their properties are consistent with their being in transit between the two regions. The relative numbers of quenched, transition, and star-forming galaxies are given as a function of mass and redshift.
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