To express the z spin state using x or y spin states, a solid understanding of the algebra of spin operators is essential. Resources such as textbooks and online course materials provide comprehensive explanations that can aid in grasping these concepts. Engaging with forums like PhysicsForums can be beneficial for addressing specific questions after initial research. It's important to approach the topic with a foundational knowledge of quantum mechanics, similar to what would be expected in a college-level course. Seeking clarification on specific challenges will yield more effective assistance.