Put on disposable latex gloves. Before you put them on, examine them closely to make sure that they don't have any holes or tears in them. When you put them on, ensure that they cover your entire hand, down to your wrist.
Wipe up the blood and bodily fluids with paper towels. The number of paper towels that you will need depends on how much fluid and blood needs to be cleaned up. Wipe up every bit of the blood and fluid. When you are done, put the paper towels in a garbage bag.
Disinfect the area. Bleach is the best thing to use, because it kills hepatitis B as well as the HIV virus. Make a disinfecting solution by mixing 1 ounce of bleach with 9 ounces of water. Cover the entire area with this solution.
Dispose of the gloves and the paper towels. Put them in the same garbage bag that you used earlier. Remove the gloves last. Do not get any of the blood or fluids on your skin. Secure the top of the bag with a twist-tie.
Place the garbage bag with the contaminated waste into a leakproof container. Label it as a biohazard. Contact your city government to learn the best way to dispose of hazardous waste. Most cities will have a Hazardous Materials Department that will come and pick it up.
Wash your hands thoroughly. Use soap and hot water. Wash with the soap and hot water for a minimum of five minutes. Dry your hands when you are done.