We have built and operated an atom interferometer of the Mach-Zehnder type. The atomic wave is a supersonic beam of lithium seeded in argon and the mirrors and beam-splitters for the atomic wave are based on elastic Bragg diffraction on laser standing waves at 671 nm. We give here a detailed description of our experimental setup and of the procedures used to align its components. We then present experimental signals, exhibiting atomic interference effects with a very high visibility, up to 84.5 %. We describe a series of experiments testing the sensitivity of the fringe visibility to the main alignment defects and to the magnetic field gradient.