In simplified terms, the Miranda rules go like this:  The police must Mirandize a person when the person is involved in a custodial interrogation.  This means

1. The person must be in custody and;

2. The person must be subject to interrogation.  Custody is defined generally as- a reasonable person would not feel free to leave, and interrogation is defined generally as express questioning or the functional equivalent- a statement that a reasonable person would expect an response/answer to. 

The way the Miranda rules play out in reality are as follows:  Officers often do not arrest a person until after they question them.  You may have seen/heard this on the T.V. show COPS.  "You are not under arrest, I am just detaining you... This way, the officer is not subjecting the person to custody under the Miranda rules and therefore does not have to inform the suspect of his or her Miranda rights prior to questioning.  The actual Miranda rights that must be provided if a person is in custody and is being interrogated are:

1. Right to remain silent;

2. Any statements can be used against the person in court;

3. Right to consult with an attorney;

4. If indigent, an attorney may be provided for them at no cost.

Common issues that arise when a criminal case goes to trial or might go to trial include:

1. Was the defendant in custody

2. Was the defendant questioned or did he or she make a voluntary statement

3. Is there an exception to Miranda including public safety

4. Did the suspect make an equivocal  (ambiguous) statement in an attempt to invoke his right to an attorney

Remedy

If there is a violation of Miranda, an the defense attorney convinces the judge of the violation, the remedy is that the statements made by the suspect prior to being mirandized cannot be used at trial.  This means that the prosecution can still use other evidence of the crime but is barred from any statements made by the defendant when he or she was subject to custodial interrogation and should have been mirandized but was not.  *Note, this is a basic overview of Miranda rules and does not address the common issue of a suspect getting Mirandized and then later making a statement regarding the same or a different crime.