Final answer:
Nurses should dispose of used needles in a puncture-resistant container located in the patient's room without recapping or altering the needle.
Step-by-step explanation:
The correct way for a nurse to dispose of a needle after giving an injection is to follow the best practices of medical waste disposal to minimize the risk of needlestick injuries and contamination. Specifically, the nurse should dispose of the syringe and needle in a rigid, puncture-resistant container that is typically found in patient's rooms for this purpose.
These containers are designed to be tamper-proof and should be located near the site of use to avoid transportation of used needles across different areas, which increases the risk of injury and contamination. Once deposited, the needle and syringe should not be recapped, bent, or broken, to further reduce the potential for accidents.