Do not say a word to the officer. Shut up. I cannot stress to you the importance of this rule. Do not talk! Do not attempt to convince the officer of your innocence. Everyone is innocent (unless and until proven guilty) no one should be arrested and no one should be in jail and that is all the officer hears all day every day. He / she does not care generally whether you are innocent or guilty and there is nothing that he / she can do at this point. Most times, when people speak to officers they say something that makes their situation far worse. Keep your mouth shut, there will be plenty of time to talk later.
Follow the cop's instructions except for answering questions. Do not be scared and do not let the liquid courage (alcohol) convince you that you can outrun the twelve officers and helicopter that will track you down. Also, police become highly suspicious that someone running has a weapon and may be quick to draw their weapon. Additionally when they do run you down expect much stronger force used to subdue a fleeing suspect. Also, if you run, expect felony charges.
Don't believe the police
Police officers are allowed to lie to get you to make an admission. The police frequently separate two friends and tell one the other one ratted him / her out. Because of the lie, the other friend now rats the first friend out. Police and detectives also state that "it will be easier" to talk now. Not true. I have had cases where police officers tell a person that their house is on fire so that the person will come out of the house.
Don't resist arrest!
Perhaps the most important thing not to do is touch the police officer at all! Many people attempt to bump the officer or swat an officers hands away. This often falls under the assault statutes and now a minor misdemeanor arrest becomes a FELONY. Thus a simple charge like reckless driving leads to much more serious charges.
Don't consent to a search.
The 4th Amendment states, "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated." Do not allow the a police officer to search anywhere! Just say, "I do not consent to a search" If the police officer asks, they do not have the right to search and must have your consent. If you are asked to consent, make sure you say to any witnesses that "You (the police) do not have consent to search." If they perform the search anyway, that evidence may be thrown out later. Know your rights. If the police have the legal right to search, they will use it. Also, if you consent to a search, the officers may find something that you had no idea you had placed somewhere, ie: marijuana left by a friend.
Do not mouth off or insult the police.
Even if you have been wrongly arrested and the true culprit is standing in front of you. Be calm. Be cool. Police hear all day that people have connections or that you will file a complaint against them. Police have a lot of discretion in the upcoming charges brought. Police can add charges, change a misdemeanor to a felony, or even talk to the prosecutor that is ultimately prosecuting you, so if you are calm and nice, that may help you.
Do not give police consent to enter your home
If the police are confident you have committed a felony, they are coming in anyway, because they generally don't need an arrest warrant. Make it clear to the police by stating: "No you may not come in", or "I am comfortable talking right here", or "You need a search warrant to enter my home." If they return, your attorney can arrange for you to turn yourself in should that be necessary and you will spend no time in jail between the hearings.
BONUS RULE FOR DUI's
Be respectful, don't answer questions, don't take the field sobriety tests and if you are over 21, do not take the Preliminary Alcohol Screening Test (PAS). If you are impaired, you are probably going to be arrested anyway, so you might as well not give them the government all the evidence they need to convict you.