If you are being arrested, the police must tell you your Miranda rights if they intend to ask you questions. If the police are asking you questions and you think you are involved in a crime, you should tell them that you do not want to answer questions until you see a lawyer, even if they have not yet read you your Miranda rights. You can insist on a right to an attorney.
When it comes to warrants, the police have some rights to search you or your residence even if you’re not under arrest and they do not have a warrant. If the police search you or your home unlawfully, then anything they find may be inadmissible at trial.