Like many websites, newspapers need content.
A lot of newspapers, especially smaller local newspapers, have a hard time coming up with enough fresh content to fill all of the space they have. With limited budgets, they do not have the staff needed to come up with fresh material every day.
This creates a great opportunity for you.
While papers are not just going to give you free advertising, they will allow you to write an article about something that your businesses is doing, especially if it involves a service or a community event.
The newspapers understand that they are allowing you to advertise in exchange for the free content, but it cannot be blatant advertising. All you have to do is write the article, making sure you mention your businesses name, and list your web address so they can get more information.
You just have to make sure the piece is well written, and that your business is doing something worth telling people about. Not only does this get the name of your business out to the community, but it also helps enhance your reputation.
Even without knowing you, people will make a judgment on whether they like you, and can trust you.
By building a positive reputation as someone who is active in the community, it makes it easier for them to like you, and by extension, your business.