In simplest terms: You find a chemical that is made of a mixture of oxygen and anything else, and then cause the molecules of that chemical to give up their oxygen (and thus becoming something else).
2 H₂O can be cracked into 4 H₂ + 1 O₂ by electrolysis
2 CO₂ can be cracked into 2 C₂ + 2 O₂ by highly inefficient electrolysis, or via photosynthesis.
2 CO₂ can be cracked and recombined to 2 CO + 1 O₂
Hematite and Iron Oxide (both of which are common) can be (given enough energy) cracked to release the oxygen, and result in iron and oxygen.
- 2 H₂O can be cracked into 2 H₂ + O₂ by electrolysis
- CO₂ can be cracked into C + O₂ by highly inefficient electrolysis, or via photosynthesis.
- 2 CO₂ can be cracked and recombined to 2 CO + O₂
- Hematite and Iron Oxide (both of which are common) can be (given enough energy) cracked to release the oxygen, and result in iron and oxygen.