Red blood cells contain a red pigment called hemoglobin which combined oxygen to become oxyhemoglobin and then once those red blood cells have traveled around the body to the tissues the oxyhemoglobin can split back into hemoglobin and oxygen again so that the oxygen is free to diffuse into our tissues.
Red blood cells have two adaptations that contribute to their role in transporting oxygen: they don't have a nucleus which means that there's more space for hemoglobin and oxygen, and they're shaped like a biconcave disc which gives them a large surface area for absorbing oxygen.
Platelets are small fragments of cells in our blood waiting until we get a cut at which point they rush to the wound and act like a glue patching up the hole.
Plasma, which makes up just over half of the blood's volume, is a liquid that carries just about everything including the red blood cells, white blood cells, and platelets.
Plasma carries nutrients like glucose and amino acids, waste products like carbon dioxide and urea, as well as hormones, proteins, and the antibodies and toxins produced by the white blood cells.