This picture gives a good example of the roles of both parties.
The dog is made complete with his tail it is an essential part of his identity.
Tails can be made from a wide source of materials. Typically thy are bonded into a butt plug, and are either horse hair, through to fur replica - there are also piggy tails if this is where the slaves head space is normally located.
The tail could also be attached to a body harness or to a piercing down there.
A word of caution, it can be very tempting for others to yank the tail, or if someone steps on it when the pup moves. They would not know that they have just yanked out the pups piercing or damaged his sphincter, thinking ahead would placate these problems.