Have you been detained or arrested? Knowing your rights is crucial to the outcome of your case.
Your rights mean very little if you don't choose to exercise them. Law enforcement either caught you in the commission of an offense or they have an arrest warrant. Either way, your case is not closed and the officers/ agents are still investigating. Their goal is to develop evidence in support of a crime because they are investigators. Prosecutors charge crimes based on the evidence obtained by law enforcement. The evidence will be used against you in the proceedings.
Law enforcement will want to "get your side of the story" after advising you of your Miranda rights. This is not the most accurate description of what law enforcement is really doing. In reality, they want you to confess because that will aid the prosecution significantly in proving the charges at trial, as well as pressuring you to accept a plea offer. The police are allowed to trick you into making incriminating statements. By contrast, you can be charged with a separate crime for lying to law enforcement. So what should you do?
The answer depends on what your goals are. Maybe you know there is a mistake and they really have the wrong person. It might make sense to speak to the officers so you can begin the process of trying to demonstrate that mistake. Because invoking your right to an attorney will likely lead to your arrest and detention. However, to avoid any more evidence being developed at your expense, you need to exercise your rights out loud. Ask if you are under arrest.
If the answer is no, you should confirm that you are free to leave and walk away. Of course, do not run away or get involved in a confrontation. The police are going to arrest you if they want to so don't make matters worse.
If the answer is yes, tell the officer that you are exercising your right to remain silent AND your right to have an attorney present for any questioning. Do not start answering questions or trying to share pieces of information in the hopes that you're going to talk your way out of something. They are there to gather evidence and you continuing to talk is their goal. Despite what you see on TV, that does not mean that an attorney is going to magically appear and you will have a chance to run through the case right there at the station. It means you are going to jail and will appear in court soon. At that point, you will have a chance to hire an attorney or the court will assign an attorney to represent you. You and your attorney will go from there. They will be grateful if the evidence in your case does not include a confession.