The PutItem operation in DynamoDB starts by receiving a request with a table name and an item to add. It first checks if the specified table exists. If the table is found, it validates the item format to ensure it has the required primary key. Then, it inserts the item into the table or replaces an existing item with the same key. Finally, it returns a success response to confirm the operation completed. If the table does not exist, the operation stops and returns an error. This process ensures items are correctly added or updated in the database.