In this paper, a molecular dynamics simulation of surfactant self-assembly using realistic atomistic models is presented. The simulations are long enough to enable the observation of several processes leading to equilibrium, such as monomer addition and detachment, micelle dissolution, and micelle fusion. The self-assembly of DeTAB surfactants takes place in three stages: fast aggregation of monomers to form small disordered oligomers; ripening process by which larger aggregates grow at the expense of smaller ones; slower stage involving collisions between large micelles. The first two stages were described well by a simple kinetic model with a size-independent rate constant estimated from the self-diffusion coefficient and collision radius of an isolated monomer. The average cluster size, area per headgroup, degree of counterion dissociation, and critical micelle concentration estimated from the simulation are in reasonable agreement with experimental values. An all-atom and united-atom surfactant model were compared, and the results were seen to be almost independent of the choice of model. DeTAB micelles are spheroidal, with a hydrophobic core composed of tail atoms surrounded by a hydrophilic corona of head atoms. A Stern layer composed of bromide counterions was also identified. Water molecules solvate the counterions and the head atoms, penetrating into the micelle up to the location of the atom connecting the head to the aliphatic tail, in agreement with recent experimental observations.