Recently, translocations of polyelectrolyte molecules through membrane channel protein pores or solid-state nanopores have been actively studied. Although the polymer translocation researches emerged mainly due to technological demands in terms of genome sequencing, the detailed physics of the single molecule transport through a narrow channel remains fully understood. To obtain further understanding of common features of the translocation process, this thesis focuses on the effects of salt concentration, pore-polymer electrostatic interactions, and externally applied electric field on the voltage-driven polymer translocations. The study is carried out by performing a series of systematically designed experiments using alpha-hemolysin (αHL) protein pore to investigate the salt concentration effects on the frequency of polymer capture by the pore and those on the subsequent polymer translocation process under various externally applied electric fields and pH. First, we demonstrate that the polymer-pore electrostatic interactions are important in dictating the rate of polymer capture by the αHL pore, controlled by the salt concentration in the donor (cis) compartment through charge screening effects. Upon the presence of a salt concentration asymmetry between the donor and the recipient (trans) compartments, the polymer capture rate is observed to be governed by coupling between the polymer-pore electrostatic interactions and additional enhancement in the electric field arising from the salt concentration asymmetry. Next, we study salt concentration effects on dynamics of polymer threading process, by measuring durations of successful translocations in various salt concentrations in cis and trans under different pH. We find that salt concentrations in cis and trans influence the polymer threading process differently, depending on pH. A theoretical model is employed to demonstrate that the charge density of the polymer chain inside the pore is a critical factor in controlling the translocation process upon varying the salt concentrations. Lastly, a new methodology to evaluate molecular weight distributions of polyelectrolyte solutions is proposed using the polymer translocation technique is proposed. The experimental results demonstrate that the translocation technique can be a competitive method for estimating the broad molecular weight distributions of polyelectrolytes in comparison with conventional mass spectroscopy techniques.