Do not resist arrest. Even if the underlying arrest is illegal you may still be charged with resisting arrest.
Give limited information.
Give only the name, address and telephone number of yourself, your immediate family and your employer. This information will be needed in setting bail.
Exercise your right to remain silent and request an attorney.
Do not give any explanation or excuse for the underlying charges or for your request for an attorney. Do not say anything, sign anything or make any decisions without talking to a lawyer.
Don't give any more information than needed during booking.
Booking is often a more relaxed stage of your arrest and you may be tempted to give more information than needed at this point. Remember, only give biographical information and the information that is needed to set bail. Suppressing statements made during booking is extremely difficult.
Call your attorney.
You have the right to make one phone call. The government will likely be listening to this phone call. However they are not allowed to listen to the call without notifying you if you are speaking with an attorney. It is advisable that your attorney is your first phone call and from there he can notify your family and any other persons who may be able to help.
You may be offered a lie detector test or other options of "clearing yourself". My general advice is not to accept these offers without talking to an attorney first. The people administering these tests are employed by the government and often the most skilled interrogators they possess. You may be subject to interrogation without even knowing it.
Most unwinnable cases become that way because of statements made after arrest.