In most DUI investigations, the main evidence in determining whether there is probable cause to arrest is a battery of "field sobriety tests". Of course, if the officer administers the test incorrectly (as is commonly the case), the results are invalid — and an innocent person may be arrested.
So what is the correct way to give the tests and interpret them?
It's all laid out online (pdf) in the 165-page DWI Detection and Standardized Field Sobriety Testing Student Manual (2004 edition), published by the National Highway Traffic Safety Administration (USDOT) and widely used for training by law enforcement agencies nationwide. Read it and understand why few officers do it right.
(Thanks to Doug Hazelton.)