Find out what frequency they are on first. If they don't tell you then go to your nearest radio shack and most of those guys know the local frequencies to everything. They will also stear you in the right direction of a scanner. Get a hand held so that you can take in the house or office, and in your car IF (and only if) you have a permit to do so. (this can be obtained from your state, I had to apply to MSP for mine).
As far as when you get on the scene, mostly just stay out of our way. Say it is an accident....get on scene, park way out of the way of ambulances (maybe a near by parking lot) and walk to the scene. Just take your pictures and maybe talk to some people, don't bother the officer, especially if he is helping extricate someone. Talk to one of the lonely fireman that is standing around, they often are starved to get their names in the paper. After you have judged the scene and it is settled down you can ask the officer (maybe when he is in the car writing). You will develop a repor with your police, I know most of the area reporters and they know that if they come up to me all they have to do is ask nicely and i'll tell them if I have time or not.
Just be smart, don't go in to shootings and major crimes in progress, and most of all be safe.
"ching ching, pull it over buddy. You're under arrest...get in the basket." ~ Super Six 5