I'm a former news photog ... small publications are easier to crack than larger. The larger the paper the more news worthy and better quality the photo.
Some tips- smaller papers have minimal staff on weekends ... so less competition from staffers and "stringers" (no spinners ... spinners are on hub caps.)
Hard news has a better chance than a feature photo. Get caption info, who, what , where, when, why, ID's of people involved (Left to Rights.)
Typically, no money, but you should get a photo credit. Paper will probably asked you to sign a release authorizing the paper to use your photo.
Persistence will ultimately prevail. After a few images get published you will have established a relationship with the paper making it easier to get your stuff published and they they even call you when no staffers are available (a stringer.). Never misrepresent yourself to those involved at the scene. Just call yourself a free lancer and identify the paper you will call/potentially publish. Never step past the police line and always stay on public property until you are probably credentialed. Always have a pad and pen for taking notes and IDs ... a business card would be helpful.
You may/will run into a lot of crap (depending on the size of the city) ... Always be courteous or just ignore the crap. Always ... Always look and act professional. Do not wear shorts or T-shirts with writing. Look and watch before you leap. Do not interfere with first responders or members of the working press if they're busy ... if you need info ask for the PIO. Most news people will talk to you just wait for a break in their action to approach them. Remember that you're there for fun, the first responders and press are there professionally and the victims are having their lives turned upside down.
Good Luck and Good Shooting,
Gary