First here is the big answer of what we have to start with on Mars. This is from the Atmosphere of Mars Wikipedia article.
This pressure is well below the Armstrong limit for the unprotected human body. Mars's atmospheric mass of 25 teratonnes compares to Earth's 5148 teratonnes; Mars has a scale height of 11.1 kilometres (6.9 mi)  versus Earth's 8.5 kilometres (5.3 mi). 
The Martian atmosphere consists of approximately 96% carbon dioxide, 1.9% argon, 1.9% nitrogen, and traces of free oxygen, carbon monoxide, water and methane, among other gases,  for a mean molar mass of 43.34 g/mol.   There has been renewed interest in its composition since the detection of traces of methane in 2003   that may indicate life but may also be produced by a geochemical process, volcanic or hydrothermal activity. 
There are several ways that might work.
- Concentration on the atmosphere on Mars
the 1.9 % oxygen and 1.9 % argon components of a breathable atmosphere.
- Using energy sources such as solar and geothermal to turn CO2 into O2 and CO this is and a serious
amount of energy
Here is a NASA experiment in to doing just that
How to brew oxygen on Mars
There is practically no oxygen in Mars's atmosphere, but the MOXIE device will “brew” oxygen from carbon dioxide (CO2), which there is plenty of in the planet’s atmosphere.
A carbon dioxide molecule consists of a carbon atom (C) and two oxygen atoms (O2), and it will be the job of the MOXIE apparatus to split the carbon dioxide molecules apart.
The splitting process requires energy, but the end result will be oxygen molecules and a by-product in the form of carbon monoxide (CO).
"MOXIE works like a sort of fuel cell in reverse. A fuel cell produces energy by melting together hydrogen and oxygen to produce water. Instead, we'll be using energy to remove an oxygen atom from CO2," says Madsen.
He explains that MOXIE will get its energy from a Radio Thermal Generator (RTG) which generates electricity from heat developed in radioactive plutonium.
Will provide oxygen people on Mars
Around 96 per cent of the Martian atmosphere consists of carbon dioxide so there is plenty of raw material for oxygen production.
NASA spokespersons have stated that MOXIE is only the beginning of oxygen production on Mars.
"Having the ability to produce oxygen on the surface of Mars is a great step forward when it comes to mankind's future exploration of Mars," said Michael Meyer, a leading scientist at NASA's Mars Exploration Program, to Space.com.
The plan is to build an entire oxygen factory on the red planet which will be about 100 times the size of the first MOXIE prototype which is to be launched from Earth with the Mars 2020 mission.
The prototype oxygen factory will have to be ready when NASA sends the first humans to Mars at some time in the 2030s.