While I can't draw you a diagram for this answer, I can provide a link to an online image that highlights some of the basic unique qualities to arteries, veins, and capillaries. I can also help explain the basic structure and functions of each of those blood vessels.
Arteries, capillaries, and veins are all blood vessels. Their job is to carry the blood, and all that blood carries, to and from the body's cells.
Arteries carry blood away from the heart. I always tell students to remember that "artery" and "away" both start with the letter "A," and that should help them remember the job of an artery. More often than not, arteries are carrying oxygen-rich blood because they are carrying blood away from the heart to the cells that need the oxygen in order to perform cellular respiration. The exception are the arteries involved with pulmonary circulation. The right side of the heart will send blood away from it to the lungs in order to exchange carbon dioxide for oxygen. Because arteries carry blood away from the heart, they have to be able to withstand the high-pressure environment that is created when the heart contracts. This is why arteries are made of thick, flexible tissue layers.
Veins have much thinner walls because they do not have to withstand the high pressures of the contracting heart. The heart isn't actually powerful enough to pump all of the blood back to itself, so the veins have one-way valves built into them. This ensures that the blood doesn't flow backward. The surrounding muscle tissue also squeezes veins, and that action helps push the blood along the veins much like when you squeeze toothpaste out of the tube.
Capillaries serve as a "bridge" between the smallest arteries and veins. They are extremely thin and narrow. Many capillaries are so narrow that red blood cells have to go through them one at a time. This allows capillaries access to just about every cell in the human body. Capillaries are made of very thin walls, which allow for the diffusion of gasses through those thin barriers.