How to do injective proof?

Could you elaborate on the process of performing an injective proof? I'm particularly interested in understanding the fundamental steps involved and any key concepts that need to be grasped. Could you provide an example or scenario to illustrate the concept of injectivity and how a proof is constructed? Additionally, what are some common pitfalls or misconceptions that one should avoid while attempting to prove injectivity? I'm eager to gain a deeper understanding of this topic and would appreciate your guidance.