To understand the mechanism by which individual DNA molecules enter nanometer-scale pores, we studied the concentration and voltage dependence of polynucleotide-induced ionic-current blockades of a single alpha-hemolysin ion channel. We find that the blockade frequency is proportional to the polymer concentration, that it increases exponentially with the applied potential, and that DNA enters the pore more readily through the entrance that has the larger vestibule. We also measure the minimum value of the electrical potential that confines a modified polymer inside the pore against random diffusion and repulsive forces.