How should liquid nitrogen and liquid oxygen be stored and dispensed? What safety equipment and precautions are employed?
Well, I knew a professor of inorganic chemistry who would use liquid oxygen to light a charcoal barbecue, but I don't think that is what you mean.
Liquid oxygen is a cryogenic liquid. Clearly, it is an oxidizing material, however, its very coldness presents a safety hazard. Most of the time, for instance if you were doing an experiment for a magic show, a normal thermos flask (i.e. a hollow glass tube sealed under vacuum) would allow you transfer litre quantities from the Dewar (the vessel in which the bulk liquid oxygen was stored, which is also a hollow glass vacuum flask) to wherever you were doing the experiment.
The use of thermos flasks to transport liquid nitrogen is of long standing. A chemist would wear a lab coat, and of course safety spectacles, to do any transfer.