The US Supreme Court decision in Miranda v. Arizona is still alive, though some justices on the court have indicated they would like to overturn it. However, many people don't understand what it means.
If you are arrested, the police have to inform you of your right to an attorney (appointed, if you can't afford one), your right to remain silent, and the fact that your statements can be used against you. Note that this only applies if you are actually arrested, or subjected to custody that is the equivalent of arrest.
For example, the Supreme Court says getting pulled over for a DUI, questioned and doing the "roadside ballet" isn't really being arrested, so the cops don't have to read your rights. By the time they slap on the cuffs, they usually don't have any questions left to ask, so they don't bother to read your rights.
The police may also ask you to come down and answer some questions, being very careful to tell you that you aren't under arrest and are free to leave at any time. They may be lying just so they don't have to advise you of your rights, and will arrest you when they have all the information they want. Again, the Supreme Court says that's okay.
Finally, even if the cops clearly failed to advise you of your Miranda rights, it doesn't mean the case will be dismissed. It only means the prosecution can't use any statements you made after the point where the cops should have advised you.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like Avvo, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.