As with most novels, there are a lot of literary techniques at work in this story. I'll start you off by discussing just a few of the author's main strategies.
First, the author, Amy Tan, employs symbolism to get her point across. In The Joy Luck Club, the book The Twenty-Six Malignant Gates discusses all the dangerous things that can happen to children. One could say this book symbolizes a mother's love and her desire to protect her children. It could also symbolize the ways in which mothers constantly worry about their children. Another symbol is the Joy Luck Club itself, which is a weekly meeting between women that symbolizes the importance of community and mutual support.
Second, Tan draws heavily on allegory, which is similar to symbolism in that it uses one thing to represent another thing. Allegories are stories that are meant to be interpreted to reveal their hidden meanings. Tan provides several allegories throughout this novel to explain larger concepts. For example, the fourth part of the novel features an allegory about the Queen Mother of the Western Skies, who realizes she passed down the wrong kind of wisdom to her daughter. Thus, this allegory discusses the ways in which mothers don't always know everything, and the ways that mothers can sometimes hurt their children by passing their own biases on to them, both of which are important themes in this book.
Finally, Tan writes the story using a nonlinear narrative, which means she skips around, moving forward and backward in time. She also weaves together several different characters' points of view. The literary techniques of nonlinear narratives and multiple voices woven together are important to the story's overall meaning; Tan uses these techniques partly to show us how it takes many different voices and perspectives to tell a complete story.