We theoretically consider transport properties of a normal metal (N)-superconducting semiconductor nanowire (S)-normal metal (N) structure (NSN) in the context of the possible existence of Majorana bound states in semiconductor-superconductor hybrid systems with spin-orbit coupling and external magnetic field. We study in detail the transport signatures of the topological quantum phase transition (TQPT) as well as the existence of the Majorana bound states in the electrical transport properties of the NSN structure. Our treatment includes the realistic non-perturbative effects of disorder, which is detrimental to the topological phase (eventually suppressing the superconducting gap completely), and the effects of the tunneling barriers (or the transparency at the tunneling NS contacts), which affect (and suppress) the zero bias conductance peak associated with the zero-energy Majorana bound states. We show that in the presence of generic disorder and barrier transparency the interpretation of the zero bias peak as being associated with the Majorana bound state is problematic since the non-local correlations between the two NS contacts at two ends may not manifest themselves in the tunneling conductance through the whole NSN structure. We establish that a simple modification of the standard transport measurements using conductance differences (rather than the conductance itself as in a single NS junction) as the measured quantity can allow direct observation of the non-local correlations inherent in the Majorana bound states. We also show that our proposed analysis of transport properties of the NSN junction enables the mapping out of the topological phase diagram (even in the presence of considerable disorder) by precisely detecting the TQPT point. We propose direct experimental studies of NSN junctions (rather than just a single NS junction) in order to establish the existence of Majorana bound states and the topological superconducting phase in semiconductor nanowires of current interest. Throughout the work we emphasize that the NSN transport properties are sensitive to both the bulk topological phase and the end Majorana bound states, and thus the NSN junction is well-suited for studying the non-local correlations between the end Majorana modes as well as the bulk TQPT itself.