It depends on the jurisdiction. In general, the police begin with a roadside test. This is either an standard field sobriety test (walking in a straight line, touching your nose, etc) or a screening breathalyzer. If the person fails, they are arrested and taken to the station for further testing. This is either performed using a more accurate breathalyzer, or a blood test. In general, suspects can choose which test they want (blood or breath).