We give a correspondence which associates, to each Del Pezzo surface X of degree 6 over a field k of characteristic 0, a collection of data consisting of a Severi-Brauer variety/k and a set of points defined over some extension of k. The main results in this paper, and specifically Theorem 5.1, give a way to describe Del Pezzo surfaces of degree 6 over a field k of characteristic 0, via a correspondence with objects (Severi-Brauer varieties) which can be understood in a completely explicit way if k is sufficiently nice (e.g. k a number field).