Blood has protein in it, which can cause it to stain. Blood can also be a big carrier of disease so unless you are certain of where the blood has come from treat it like you would an infectious substance. Be sure to wear disposable gloves and dispose of any absorbent materials in a plastic bag of their own. If there is a lot of blood then consider wearing a mask, gloves and protective clothing.
This might seem like a lot of precautions to take but blood is a carrier of many bacteria and diseases and it is also a nurturing base for the growth of all kinds of molds. The good news is that cleaning up blood over hard surfaces like tile, vinyl, hardwood, cement or metal floors is easier than cleaning it up off of a fabric surface.
To clean up a spill on a hard surface soak up as much of the blood as possible with paper towels or another absorbent material. Then pour a bleach solution of one part bleach to nine parts water over the contaminated area. Leave this solution on the blood stain for twenty minutes and then allow floors to dry naturally.
If there is a great deal of blood to clean up then you might have to use some kind of absorbent material to soak it up. In a pinch kitty litter can work to help soak up any excess liquid. If there is a lot of blood you should also take some kind of measure to block off or contain the contaminated area so that it cannot come in contact with pets or people.
After you are done cleaning up the blood be sure to disinfect all of the martials that you used to clean up the mess. This is especially important if you think the blood you were cleaning up was infected in any way. Disinfect any mops, brushes and rags that you intend to use again by saturating each with bleach solution and then allowing them to dry in the air. Any gloves worn should be thrown out with all other soiled cleaning materials.
When discarding blood make sure it is in double garbage bags and then throw it out. Afterwards be very sure to thoroughly wash your hands with soap and water. Ideally if the blood spill was huge it is a good idea to take a shower.