Traces of blood on and in the needle and in the syringe can contain a high concentration of HIV and other viruses and bacteria - even if the blood cannot be seen with the naked eye.
You should therefore always use your own syringe. Ideally, you should use a new syringe for every fix.
Many cities have places where you can get sterile syringes for free or for a very low price, or where you can exchange old needles for new ones. Syringe vending machines ("Spritzenautomaten") offer 24-hour access to sterile equipment.
If you are ever in a situation where you cannot avoid using a syringe that someone else has used, it should at least be boiled or disinfected.
If that is also not possible, it is recommended that you snort the drug rather than inject it. This will keep the withdrawal symptoms at bay until you can get a clean syringe.