Disposable syringes can be safely reused as long as you take reasonable
precautions. Recap both ends between uses, and discard the syringe if
dropped, dirty, or damaged (especially if the needle is bent). Discard
it when it becomes uncomfortable to use. This varies a great deal,
being half a dozen uses for some patients and several dozen uses for
others. Comfort depends far less on sharpness than on the silicone
coating applied to the needle at manufacture. Never wipe the needle
with alcohol, as this will remove the silicone coating.

Lancets can also be reused safely with the same caveats.

Syringe disposal has proven controversial. If you want to be
conservative, buy a needle clipper, get a hard plastic bottle designed
for medical waste to put the syringes in, and take the full bottle to a
facility approved for handling medical waste. Your doctor's office, a
local hospital, or a pharmacy may be able to handle it for you.
Intermediate positions use one of these techniques. At the least
conservative, cap the needle carefully and discard in trash which will
not be subject to illicit searching and possible abuse. If you have
trouble capping the needle without sticking yourself, definitely get a
bottle to drop the uncapped syringes in; a bleach bottle may be
adequate.

Local or state regulations apply in many places and limit your choices.
Know the laws for your area! Where sharps containers are required, the
pharmacy where you purchase the container will probably dispose of the
full container for you.