The liquid component of your blood is called serum, a straw-yellow solution of 90% water and 10% dissolved organic compounds and salts. Serum is slightly alkaline, with its pH held between 7.35 and 7.45. when your doctor measures triglycerides, cholesterol, etc, these are dissolved in the serum. But serum, on its own, is like the sizzle without the steak. Whole blood is a suspension of red and white blood cells floating about in the serum, with 4 to 6 million blood cells crammed into each cubic millimeter of liquid. Most of these cells, about 99.9%, are red blood cells, looking like red dots under the microscope. under higher magnification, each red blood cell has the shape of a biconcave lens. It is not a sphere, like most cells - instead, opposite sides of the cell bow inward. This is another surface area expansion trick, as described in the previous article. Most of the cytoplasm, i.e. the interior of the cell, is quite close to the cell wall, and close to the oxygen it is intended to transport. A human red blood cell is typically 7 micrometers across, 2 micrometers thick near the outer edge, and only 1 micrometer thick at the center. Oxygen diffuses throughout the interior in a flash. Furthermore, the cell has no nucleus, thus the entire space can be devoted to cytoplasm rich in hemoglobin. This protein, based on an iron atom, picks up oxygen and carries it to other tissues in the body. It is red, particularly so when oxygenated, thus giving blood its rich red color. Deoxygenated blood, traveling through the veins and back to the lungs for replenishment, is a darker red, almost reddish brown. If the patient has been exposed to carbon monoxide, the blood is an unnatural, bright cherry red, due to an interaction with CO and hemoglobin. In fact, CO bonds more tightly than oxygen, thus these red blood cells can no longer perform O2 transport, even if there is plenty of oxygen in the air.
A slim minority of blood cells are leucocytes, or white blood cells. These are too few in number to affect the color of blood. They appear as occasional white dots in a sea of red dots under the microscope. These white cells fight infection.
The Vulcans on Star Trek have green blood - green because its oxygen ferrying protein (whatever that is) is based on copper, rather than iron. So we are told early on in the Original Series. This is all science fiction, right? Not entirely. There are animals on earth with copper based blood. It isn't bright green however, but a deep blue, or perhaps bluish-green when oxygenated, and dark gray when deoxygenated. I suppose the make-up artists on Star Trek thought vivid green would be more striking.
Arthropods and molluscs contain hemolymph, a primitive analog of blood. In most arthropods (insects, spiders, small crustaceans, etc), hemolymph is not used for oxygen transport, thus the substance remains dark in color. However, in some large molluscs, such as the octopus, hemolymph is needed for oxygen transport. The copper based protein that ferries oxygen about is called hemocyanin. This is similar to hemoglobin, though it is considerably less efficient. It would not serve the needs of a running gazelle, or a flying hawk, or even a resting warm-blooded sheep. However, in cold conditions with low ambient oxygen, hemocyanin can be more efficient than hemoglobin - thus there is no evolutionary pressure for the octopus to upgrade its blood from blue to red.
so - does hemolymph have blue blood cells floating about, looking like blue dots in a clear sea? No - the hemocyanin is not confined to specific blood cells. Instead, it is suspended directly in the hemolymph, thus creating a uniformly blue liquid, even under the microscope.
The octopus, and its cousin the squid, have three hearts, one for each gill, and a central heart that serves the needs of the body. These combine to push oxygen and nutrients throughout a potentially large animal. Indeed, the giant squid (including its tentacles) can span 40 feet.
If Spock does indeed have copper based blood, it isn't the hemocyanin of terrestrial molluscs. That compound is blue, not green, and far too inefficient for a warm-blooded active mammal. In fact, it's hard to see how any copper based structure could rival the oxygen carrying capacity of iron, but who knows what might evolve on another planet. Like all the suppositions in Star Trek, it is probably best not to overanalyze - just sit back and enjoy the show.