Dispose of your medical sharps by using your own containers or special "sharps" containers.
Place used sharps into a rigid container, such as a plastic bottle or a milk carton. Then, tape the container securely shut, and tuck it into the middle of your household trash.
The most ideal method is to keep sharps out of the regular waste stream altogether, using special disposal programs such as this:
Holy Cross Hospital Syringe Disposal Program
(service of Materials Management Program)
1500 Forest Glen Road
Silver Spring, MD 20910
Dispose of plastic syringes in the same way as medical sharps, as they may be considered medical waste. These syringes typically contain heparin or saline solution for flushing IV lines for at-home patient care.
To learn more: US EPA information on disposing of Medical Sharps