  Dark Matter experiments are recently focusing their detection techniques in
low-mass WIMPs, which requires the use of light elements and low energy
threshold. In this context, we describe the TREX-DM experiment, a low
background Micromegas-based Time Projection Chamber for low-mass WIMP
detection. Its main goal is the operation of an active detection mass $\sim$0.3
kg, with an energy threshold below 0.4~keVee and fully built with previously
selected radiopure materials. This work focuses on the commissioning of the
actual setup situated in a laboratory on surface. A preliminary background
model of the experiment is also presented, based on Geant4 simulations and two
discrimination methods: a conservative muon/electron and one based on a
$^{252}$Cf source. Based on this model, TREX-DM could be competitive in the
search for low mass WIMPs and, in particular, it could be sensitive to the WIMP
interpretation of the DAMA/LIBRA hint.
