Always be respectful when interacting with law enforcement. At the same time, to be aware that when the police are questioning you about a potential crime, they are not on your side. Explaining your side of the story will not clear things up. In fact, it's best to avoid saying more to the police than you absolutely have to.
You do have the right to remain silent. You do have the right to an attorney. You have those rights and more, but constitutional law is complex. You shouldn't have to be a lawyer to understand your rights, however, and here are four key concepts you should use to protect them when interacting with the police.
Ask if you are free to go. Law enforcement cannot legally detain you without probable cause to believe you have committed or are about to commit a crime. If they do not have it, they cannot legally arrest you.
The only meaningful test of whether you are under arrest is whether you are free to go. If you are not, you have been arrested. If you have been, you should immediately exercise your rights by remaining silent except to ask for an attorney.
Don't consent to searches. In order to search you, your car or your home, police either need a warrant or a legal exception to the warrant requirement. One of the exceptions is the suspect's consent to the search. Police officers commonly ask for consent in order to avoid having to show another legal cause for a search. Do not allow them to pressure you into consenting. Tell them, firmly and directly, that you do not consent to any searches.
Exercise your right to remain silent. The reality is that suspects are usually the main source of evidence in criminal cases. Don't provide the police with the evidence they need to charge and convict you. Do provide the police with your name, address and other basic information, but resist answering any other questions whatsoever. You may have to insist repeatedly that you wish to remain silent. As awkward as it is, and as much pressure as you may feel, you will do yourself absolutely no favors if you talk.
Ask for your attorney right away and keep insisting, if necessary. You have nothing to gain by talking to the police without an attorney present. Don't believe it if the police tell you they can't help you unless you cooperate -- they are not there to help you but to collect evidence against you. Your best chance at having the charges dropped or reduced is to let your attorney work directly with the prosecutor.