We quantitatively describe the creation and evolution of phase-separated domains in a multicomponent lipid bilayer membrane. The early stages, termed the nucleation stage and the independent growth stage, are extremely rapid (characteristic times are submillisecond and millisecond, respectively) and the system consists of nanodomains of average radius approximately 5-50 nm. Next, mobility of domains becomes consequential; domain merger and fission become the dominant mechanisms of matter exchange, and line tension gamma is the main determinant of the domain size distribution at any point in time. For sufficiently small gamma, the decrease in the entropy term that results from domain merger is larger than the decrease in boundary energy, and only nanodomains are present. For large gamma, the decrease in boundary energy dominates the unfavorable entropy of merger, and merger leads to rapid enlargement of nanodomains to radii of micrometer scale. At intermediate line tensions and within finite times, nanodomains can remain dispersed and coexist with a new global phase. The theoretical critical value of line tension needed to rapidly form large rafts is in accord with the experimental estimate from the curvatures of budding domains in giant unilamellar vesicles.