Broken down to the basics, the circulatory system is a very simple pump (the heart) and hose (the blood vessels) set up. Oxygenated blood starts its journey in the left atrium of the heart. During ventricular diastole (the diastolic number when measuring blood pressure), the heart muscle relaxes allowing the blood from the left atrium to flow through the bicuspid (mitral) valve into the left ventricle. Once filled, the heart contracts during its systolic phase, pushing the oxygenated blood out the aortic valve and into the aorta.
This force from the heart (the systolic number of your blood pressure) moves the oxygenated blood through the rest of your body (the systemic circulation) via a series of arteries, arterioles and finally to the capillaries. Within the capillaries, the force of the blood flow is minimal. This low pressure allows gasses (oxygen, carbon dioxide) and other nutrients and waste products to pass through the single celled walls between the tissue cells and the blood.
Once this exchange has occurred, the now oxygen deficient blood which is also carrying cell waste products including CO2 move into the venules, then to the veins, and finally returning to the right atrium of the heart via the inferior and superior vena cava. Deoxygenated blood then travels through the tricuspid valve into the right ventricle during another diastolic phase, and then with the next systolic squeeze is pumped through the pulmonary valve and onto the lungs via the pulmonary artery for pulmonic circulation.
The blood again then travels down the lungs arterial system until they reach the pulmonary capillaries which surround each alveoli, again allowing the diffusion of gasses to occur in this low pressure environment. The carbon dioxide in the blood diffuses through the capillary and into the alveoli where it is then exhaled into the air. Simultaneously the oxygen within the alveoli from the latest inhale diffuses through the same walls into the blood stream. Finally, this now oxygen rich blood is moved through into the pulmonary vein and back into the left atrium, ready to be re-distributed throughout the body again with the next heartbeat.