The basic model that SpaceX is following is similar to Robert Zubrin's Mars Direct model.
In Mars Direct, you send a ISRU (In Situ Resource Utilization) plant first, then by the time the next Mars window comes around either you have a fully fueled return vehicle waiting, or you do not. But you know before you go.
SpaceX plans to use 2022 if they are ready to launch a cargo only mission to Mars, that would likely carry an ISRU plant to process the fuel and oxidizer. This is why SpaceX selected Methane as their future fuel, as on Mars the atmosphere is primarily carbon dioxide, which can be chemically processed (Sabatier process) to Methane if you add in some hydrogen (which you get from water, or bring with you).
Food wise, you bring everything with you.
Water wise, you need recycling anyway, so you bring enough for the mission.
Fuel/Oxidizer you expect to manufacture on Mars.
Nitrogen is possibly a problem.