Read the book, paying close attention to how groups of people are portrayed in the book. You may find that older books will have increasingly blatant gender, racial and religious stereotypes compared to books that are more recent.
Some questions to ask yourself, adapted from an article by Mitali Perkins in her article for the School Library Journal titled "Straight Talk on Race: Challenging the Stereotypes in Kids' Books," include how are non-white, female or disabled characters portrayed in the book? What is the setting, and in what time period is the story taking place?
Are all women expected to be wives and mothers, are all girls supposed to be afraid of bugs and getting their dresses dirty? Are certain negative character traits such as jealousy and gossiping specifically stated to be exclusively feminine traits?
Are all non-white characters expected to behave a certain way? Are they automatically the bad guys or the ones that are different and exotic? Are non-white characters belonging to multiple ethnic groups lumped together into one group or designation?
How are disabled characters portrayed? Are they regarded as a burden by the narrative, as helpless or inconvenient? Are the disabled described in a ways that makes them seem overtly grotesque or frightening?
Keep in mind that even seemingly "positive" stereotypes count as stereotypes. Likewise, remember that those positive stereotypes can quickly become negative. Think about how each "positive" stereotype you come across can be turned into a negative stereotype. Don't limit the questions you ask to the ones listed.