To install QUANTUM ESPRESSO from source, you need first of all a minimal Unix environment: basically, a command shell (e.g., bash or tcsh) and the utilities make, awk, sed. MS-Windows users need to have Cygwin (a UNIX environment which runs under Windows) installed: see http://www.cygwin.com/. Note that the scripts contained in the distribution assume that the local language is set to the standard, i.e. "C"; other settings may break them. Use export LC_ALL=C (sh/bash) or setenv LC_ALL C (csh/tcsh) to prevent any problem when running scripts (including installation scripts).
Second, you need C and Fortran-95 compilers. For parallel execution, you will also need MPI libraries and a parallel (i.e. MPI-aware) compiler. For massively parallel machines, or for simple multicore parallelization, an OpenMP-aware compiler and libraries are also required.
Big machines with specialized hardware (e.g. IBM SP, CRAY, etc) typically have a Fortran-95 compiler with MPI and OpenMP libraries bundled with the software. Workstations or ``commodity'' machines, using PC hardware, may or may not have the needed software. If not, you need either to buy a commercial product (e.g Portland) or to install an open-source compiler like gfortran or g95. Note that several commercial compilers are available free of charge under some license for academic or personal usage (e.g. Intel, Sun).