Most DUI arrests result from traffic stops, when a police officer pulls you over for a traffic violation (e.g. speeding, failure to use a turn signal, no headlights). Once the officer pulls you over, he is trained to look for visual clues that you are impaired. These include:
At this point, the officer will probably ask you if you have been drinking. Whatever you say can be used against you. You do not have to answer and should at that time state that you are invoking your right to remain silent.