You should first create a good web site layout for newspaper and if that is about seo then it will definitely difference from the ordinary newspaper website. If you interesting in simple advertising then you should checkout the local advertising company, newspapers and also the web site and they will place you ads in their newspapers and websites. when your website advertise locally then you should hire seo team if you interested in web level or world level advertising. They will keep your site ranking higher which is the best way to promote it and also they will advertise it on different platforms.
Crete the website with good graphics and do onpage for that. After the onpage SEO, you must promote it with strategic planning. Promote good content written for the same.
When your website will be ready you just start SEO on your website. You work slowly slowly and build natural backlinks that Google recommend. You will see that within few weeks your newspaper website will be perform well in search engine.