To add to the other answers. The process of oxygenation of the cells from the capillaries is called diffusion. Basically the capillary wall is thin enough, that it is leaking Oxygen molecules to the surrounding tissues. The rate of oxygenation depends on partial pressure of oxygen and carbon dioxide (and some other factors) in the surrounding tissues, but usually you can't diffuse farther then a few mm's in a living organism.

Diffusion is mostly used by insects as the main oxygenation process since they are small enough to just have some air filled pipes (tracheas) inside their bodies where the oxygen is directly absorbed from the air.