Assignments are made by selection of a committee that carefully reviews personalities and volunteer work.
In the community, children are given the assignments they will have as adults when they are twelve years old.
It was a secret selection, made by the leaders of the community, the Committee of Elders, who took the responsibility so seriously that there were never even any jokes made about Assignments. (ch 2, p. 15)
The children do volunteer work in the years leading up to the assignments, and the committee members watch them at school as well. They try to see which personalities work best with which jobs, so that they assign a person who will enjoy the job and be a good fit.
It seems that people are generally happy with the assignment, and no one has ever complained or felt that a bad choice was made.
Lowry, Lois (1993-04-26). The Giver (Newbery Medal Book). Houghton Mifflin Harcourt. Kindle Edition.
Assignments are "secret selections" made by the Committee of Elders in order to determine what individuals will do in their lives.
In order to make their selections, the Elders first carefully observe the individuals under consideration. Some of the observations of the children are made at school; additional observations are made of the children as they participate in their respective volunteer groups. Following the completion of their observations, the Elders meet extensively with all the instructors of each individual under consideration. Then, after the assignments have been decided, the ceremonies are held.
The ceremonies differ for each age group. The Ceremony of One, for instance, assigns the "newchildren" to family units. These "newchildren" are given names to use instead of the numbers that they have been assigned since birth. The last ceremony, the Ceremony of Twelve, is the most important ceremony because those individuals who are Twelves are assigned a career. Thus they are placed on the path that will determine the rest of their lives.
In Chapter 2 of The Giver, the approaching Ceremony of Twelve causes Jonas some anxiety. His father tries to reassure him by saying,
"There are very rarely disappointments, Jonas. I don't think you need to worry...."
Also, his mother informs Jonas,
"After the Ceremony of Twelve, you'll be with your Assignment group, with those in training. No more volunteer hours. No more recreation hours. So your friends will no longer be as close."
Although Jonas is somewhat reassured by his parents, he does not have any idea of what his Assignment will be or how he might react to it.