The phase separation process in mixtures containing two immiscible liquids and a surfactant was investigated in two dimensions by numerically integrating a time dependent Ginzburg-Landau model. The model free energy was constructed from two scalar and one vector order parameter fields. The scalar fields describe, respectively, the local density difference of the immiscible liquids and the local, surfactant density, while the vector field provides the local average orientation of the surfactant molecules. The time evolution of the characteristic domain size was studied as a function of the mean surfactant density, n(0), in systems having a 1:1 ratio of the two immiscible liquids. At low n(0), the growth law for the domain size follows nearly power law behavior, with the growth law exponent decreasing with increasing surfactant concentration. As n(0) was further increased, the growth rate for the characteristic domain size at intermediate to late times was found to be significantly slowed, in agreement with previous theoretical investigations. The slow growth is attributed to the accumulation of surfactant at the interface between the immiscible liquids, which leads to a reduction in the surface tension between the immiscible liquids. We found that the surfactant moves to the interfacial region very early in the phase separation process; however, the interfaces are not uniformly coated with surfactant. Dynamic scaling was observed at late times for the range of mean surfactant densities considered.