Oxygen moves through the cell membrane through a process called diffusion. Diffusion can be described as the molecules movement from a higher concentration region to a region of lower concentration. This means that oxygen will move from outside the cell into the cell because there is more oxygen outside the cell than inside it. Oxygen is transferred via cell plasma.
Furthermore, because it is a small molecule, oxygen can move across the cell membrane through passive transport. This means that it doesn’t exert that much energy.
The transportation of oxygen is facilitated by the hemoglobin found in red blood cells.