First of all, even if you have some illegal substance on your person, never, ever try to run or resist arrest in any way.  That course of action will almost certainly makes things worse for you.  If arrested or stopped, remain quiet, polite, and cooperative, answer basic questions about your identity (name, phone number, address, etc.), and produce such documents as license and registration when asked.  Beyond that, keep your mouth shut.  Do not get belligerent and "demand" a lawyer, but do feel comfortable with your right to say, "I would like to talk to my attorney."
 
It is a common and understandable desire to try to explain your side of things to the police officer in hopes that he or she will let you go.  But it just does not work in 999 out of a thousand cases, because the officer is more likely to leave that decision to the prosecuting attorney.  So, for example, it will not help you to say "Officer, I only had one drink."  All you are doing is providing evidence for your future prosecution by admitting that you have consumed alcohol (even if you are telling the truth about the one drink, it is still possible to be convicted of driving under the influence after consuming only one drink).  So, when the officer starts asking questions not related to your identity, simply state that you would prefer to talk to your attorney.  Good luck, and may you never need the information in this answer.