That is the correct way to give a handjob.
The act is carried out by firmly placing the hand around the shaft of the penis and then moving it up and down. This is continued until ejaculation takes place. The testicles are generally caressed as well by the other hand.
Also referred to as "choking the chicken", "wanking", "wanking your wood", "tugjob", "jacking off" and "jerking off".
Most commonly preferred to be performed by a female on a male. Some females will "offer" a handjob instead of intercourse, or to avoid intercourse, or oral sex. Some females desire to perform "handjobs" for the sole purpose of being able to observe the male ejaculation ( which some find stimulating)and/or desire the ejaculation to land on the female body.
The handjob may be performed in a variety of postions as long as the female can reach the penis.
It is commonly used as form of quick sexual release for the male and may be performed almost anywhere at anytime. Often used as a quick substitute for when intercourse may not be practical.
When I am not in the mood, I'll give him a handjob instead.
I gave him a handjob while he was driving the other day.
C'mon baby, at least give me a handjob if you won't fuck or suck!