People fill their lungs with air periodically, It looks like about 1 cubic foot per minute, regardless of the density (mass) or content. This, of course depends on exertion level.
In tabular form this is:
Activity : Respiration per Person in m3/h (cuft/min)
Sleep : 0.3 (0.18)
Resting or low activity work : 0.5 (0.29)
Normal work : 2 - 3 (1.18-1.77)
Hard work : 7 - 8 (4.12-3.71)
These correspond roughly to personal scuba diving experience.
The easiest way to produce this volume is with a simple scba/scuba type breathing rig. A pressurized tank supplies a face mask via a regulator. A valve allows the breathing gas in, and the exhaled gas gets dumped to the local atmosphere.
At Normal earth pressures (14.7 psi) and temperatures, the density of the air is about 1.15 kg/m^3. This means a Normal person at normal work is going to use approximately 3 kg (6 lbs) of air per hour.
Although this seems pretty wasteful, it's simplicity is good, with all the waste water, CO2, or other pollutants pushed permanently away from the people. For short durations, this may be the best way to go.
To improve the analysis, it is necessary to realize that most spacecraft cabins are at considerably less than 15 psi, Advanced space suits can only be pressurized to about 8 psi, with more primitive ones being considerably less (tough to move!). If we assume a cabin pressure at around 5 psi (with plenty of O2) then the consumption goes down by about two thirds.
At 5 psi cabin pressure should use about 2 lbs of oxygen enriched air per person per hour.
There is plenty of improvements to be made in the consumables, but they require a more sophisticated (complicated) system that takes into account CO2 removal and Oxygen supply. Additionally you have the storage method for the breathing gases. Simple scuba tanks are very heavy for the amount of air they hold.