In recent years there has been considerable effort to experimentally realize new exotic excitations known as Majorana fermions, that may be useful for topological quantum computation. In the context of condensed-matter physics, Majorana fermions were originally conceived as particles which are bound to vortices in a 2D p+ip superconductor. However, in face of the great difficulty in experimental realization of such a 2D system, it has been recently suggested that Majorana fermions can appear in a more easily obtainable 1D dimensional system as well. This 1D system takes the form of a semiconducting nanowire with strong spin-orbit coupling, made superconducting due to a proximity effect, subjected to a magnetic field and a tunable gate voltage. By tuning the different parameters one can bring the wire into nine different phases, one of which is Kitaev's spinless p-wave topological superconducting phase that supports Majorana fermions at its edges. We present an analysis of the different phases of the wire, which includes calculations of the tunneling density of states of the different phases. Moreover, we present conductance calculations of several heterostructures of the different phases of the wire, and show that the ones that are predicted to support Majorana fermions display a unique signature in their conductance.