  Our understanding of physical properties of quasicrystals owes a great deal
to studies of tight-binding models constructed on quasiperiodic tilings. Among
the large number of possible quasiperiodic structures, two dimensional tilings
are of particular importance -- in their own right, but also for information
regarding properties of three dimensional systems. We provide here a users
manual for those wishing to construct and study physical properties of the
8-fold Ammann-Beenker quasicrystal, a good starting point for investigations of
two dimensional quasiperiodic systems. This tiling has a relatively
straightforward construction. Thus, geometrical properties such as the type and
number of local environments can be readily found by simple analytical
computations. Transformations of sites under discrete scale changes -- called
inflations and deflations -- are easier to establish compared to the celebrated
Penrose tiling, for example. We have aimed to describe the methodology with a
minimum of technicalities but in sufficient detail so as to enable
non-specialists to generate quasiperiodic tilings and periodic approximants,
with or without disorder. The discussion of properties includes some relations
not previously published, and examples with figures.
