The police have the right to try to question people. If you have been told that you are "under arrest" then you are in custody. If you are otherwise not free to leave and go home you are physically being detained and under arrest. Miranda warnings/rights are only implicated and become relevant if you are under arrest. Questioning by an officer for example in your front yard does not implicate Miranda warnings and the officer has no obligation to advise you of your rights. Also, if you have been placed under arrest and the officer does not try to interrogate you he/she does not have to advise you of your Miranda warnings.
Having been placed under arrest and advised of your Miranda rights means that from that point on you have no obligation or duty to speak with the police. If you decide that you do not wish to speak to the police than you should simply state that I am exercising my right to remain silent. Remember, you post-arrest silence can not be used against you at trial. However, silence is just that, silence; if you begin speaking to the police on your own after having invoked your right to remain silent the law states that that can be viewed as your waiving your Miranda rights and an exercise of your choice to make statements to the police, which can trigger questioning by the police.
Deciding to speak
If you decide to waive your Miranda rights and speak with the police, (not recommended), understand that your statement can be memorialized in two ways. 1) It can be audio and/or tape recorded. 2) It can be set forth in a police report as a "narrative"; this is where an officer takes notes and paraphrases in writing a generalization of what you told him/her. If you are going to waive your Miranda rights and speak with the police without the benefit of having counsel present, (once again, never recommended), you should INSIST on going into the station and having your entire statement electronically recorded. This helps to avoid a situation where you end up trying to claim that what the police are saying you said you did not say; or, leaving you to try to explain that your remarks were taken out of context. This is a frequent observation made by Defendant's when their statement has been preserved by notes and reconstituted in narrative form.