Capillaries have holes, called pores, in 'em (which can be made bigger or smaller by chemicals in your body I won’t go into here.) So the oxygen gets glommed onto a hemoglobin molecule in the red blood cell, and it goes for a ride through your heart and then up your aorta and out to the smaller vessels in the circulatory system.
When it gets to a place where there’s low oxygen (so it’s not like a bucket brigade, but rather nearer places to the heart get served their oxygen first), the oxygen detaches from the hemoglobin, moves out of the red blood cell (through pores in the cell wall), and through one of the holes in the capillary wall.
It doesn’t go directly into the cell from the capillary, but into a space between the capillaries and the cell. This space is called “interstitial space”. From there, it goes into a cell that’s low on oxygen.
Meanwhile, when carbon dioxide builds up in a cell, some of it leaves the cell and goes into the interstitial space, and then when the blood in the capillary has less carbon dioxide than the interstitial space next to it, the carbon dioxide moves into the blood through holes in the capillary, where it’s taken back to the heart, then to the lungs, and the carbon dioxide again moves into the interstitial space of the lungs, then into the alveoli of the lungs, then you can exhale it.
Ditto for all the other nutrients and wastes of the cells. Nutrients move from the digestive tract into the interstitial space, into the capillaries, into different interstitial space and then into cells. Wastes go from cells to interstitial space to capillaries to interstitial space to bladder or bowel. It all has to do with diffusion. Where a concentration is higher on one side of a membrane than the other, the substance will pass through a hole in the membrane.
Interstitial space isn’t generally taught until A&P II, but it makes everything you’ve been learning in chemistry and biology until then suddenly make sense. It’s what makes diffusion (and osmosis) actually happen, because it provides for different concentration gradients in a very close proximity.