Space is mostly empty, just nothingness. So you don’t get the privilege of having “free air" in space, you will have to take it there with you, just like you take sandwiches to a picnic.

There primarily two ways in which oxygen is produced/stored in space. One is obvious storing it in high pressure gas tanks. Another is method is oxygen production from electrolysis of water. Water (H₂O) is made of two parts hydrogen (H₂) and one part Oxygen (O₂), and applying electricity (generated by energy from the sun, in space) to it should split and separate out O₂ from H₂. H₂ that comes out is let out into space or combined with carbon dioxide, CO₂ (exhaled by people) to produce water, which is reused, and methane (CH₄), which is let out.

NASA, of course, has thought a lot about this, and is trying to make the process more natural, as we have here on earth, by creating symbiotic relation between humans and photosynthetic organism- plants, algae,...read more here