I want to do respiration process of an animal cell media in laboratory environment.
I don't entirely sure how to supply it with Oxygen to the process because it is a gas, but not a liquid.
Supply of cells growing in adherent culture is unproblematic, as long as you don't fill too much media in the petri dish/cell culture flask.
Oxygen supply here work by diffusion which is getting more problematic if the layer of media covering the cells gets to thick. I usually follow the recommendations of Corning for the amount of media to be used in the flasks/dishes:
The complete information can be found here, other companies have similar data sheets available. With these amounts I do a lot of cell culture work and I have no growth problems.