This is sort of a broad question...
The book is not set in any particular place or time. The society is somewhat futuristic, but we don't know exactly how far in the future it is.
The book is set in a society where people have been robbed of all their choices and their emotions, more or less. They essentially have no families and they have no sexual urges. They are assigned jobs and children. Their whole lives are pretty much controlled by the government. This has gone so far that the people are not even able to see in color.
So the setting is not in a certain time or place -- it's more of a general atmosphere or mood.
The setting in the book "The Giver" is a community. The community consists of single family dwelling, a nurturing center, an old folk’s residence with an annex, a school, and some other structures. The buildings are colorless and so are the people and their clothing. Color has been taken away and placed in the Giver's memories. All the people wear the same thing with the exception of some different items. Certain age groups have different items to tell what age they are such as ribbons in their hair or buttons on their clothing. Everything is controlled by the government consisting of the elders. Somehow the people are always being watched. Their actions in public places are made known over a loud speaker. The loud speakers are placed so that they can be heard throughout the community.