Membrane transport proteins actively transport ions, metabolites, drug molecules, and others across the amphiphilic cell membrane. The Major Facilitator Superfamily (MFS) is an important class of membrane transporters whose members are found in almost all types of organisms. The MFS proteins transport a diverse range of molecules including sugars, peptides, and drug molecules. In this work, lactose permease (LacY) of E. coli, which transports galactosides across the plasma membrane by the proton symport mechanism, is studied as a model for the MFS proteins. First, a hybrid two-step simulation approach was developed to determine the unknown periplasmic-open structure of LacY starting with the cytoplasmic-open x-ray crystal structure. A periplasmic-open model for LacY that agrees with several indirect experimental measurements was obtained. Sugar binding and protonation of Glu269 were found to be the triggers for LacY's structural change from the cytoplasmic- to the periplasmic-open state. Mutations in residues Asn245, Ser41, Glu374, Lys42 and Gln242 to prevent cross-domain hydrogen bonding were proposed that might aid in crystallizing LacY in the periplasmic-open state. The second focus of this dissertation was a comprehensive study on the binding of high- and low-affinity binders as well as non-binders to LacY in its cytoplasmic- and periplasmic-open states. A possible pathway for the substrate translocation, which involves aromatic stacking interactions of substrates with Phe354 and Tyr350, was suggested. Binding free energy values calculated using the alchemical free energy perturbation method agree with the experimental data. The differences in binding affinities result from dissimilarities in the binding structures of different sugars. The binding free energy values as well as the binding structures in the cytoplasmic- and the periplasmic-open states of LacY provide a quantitative proof of the alternating access mechanism in LacY. Lastly, hybrid quantum mechanics/molecular mechanics (QM/MM) studies on LacY were performed, which are the first QM/MM studies of proton transport in an MFS protein. These QM/MM studies suggest an important role of water molecules in proton transfer. A hydronium ion intermediate was observed during proton transfer from Glu325 to His322, which is consistent with the experimental hypothesis. The transfer of proton from His322 to Glu269 was found to be the rate-determining reaction. More extensive QM/MM calculations on LacY are proposed to fully probe proton translocation in this protein. This dissertation has touched all the important aspects of LacY's transport cycle and results from this study can be beneficial for understanding the mechanism of other MFS proteins such as the drug efflux protein EmrD, which shares its structural and functional motif with LacY.