United-atom Langevin dynamics simulations have been performed in an effort to understand early-stage polymer crystallization at the microscopic level. We have modeled the crystallization process by following the competition between the attraction among nonbonded beads and torsional energies along chain backbones. We have monitored three processes : spontaneous formation of initial nuclei and their subsequent growth in time by an isolated chain as a function of degree of undercooling, crystallization at a growth front as a function of commesurability between the thickness of the growth front and the length of crystallizing chains, and cooperative crystallization by several chains into lamellae. The details of growth kinetics here have been captured by explicit visual displays of chain conformations, radius of gyration of labeled chains and aggregates, local and global orientation order parameters, and interaction energies all as functions of time. We observe that the kinetic pathway of lamellar thickening is stepwise and quantized for small degrees of undercooling and that the lamellar thickness is inversely related to the degree of undercooling. The crystallization is found to be more efficient if chain length is an integer multiple of the thickness of the growth front. We have compared several of our key simulation results with experimentally observed results reported in the literature and found that the simulations exhibit many salient features of polymer crystallization in dilute solutions.