You won’t need much to start publishing your own newspaper online. You'll need access to a computer with an Internet connection. If you are going to publish pictures (and why wouldn't you?), you'll need a digital camera that can connect to your computer or that uses a card that your computer can read. Most new laptops and desktop computers have card readers built in.
Perhaps the most important requirement is a strong desire to be a part of the publishing community. Frankly, this involves a lot of hard work. Unless you're buying all of your content, you'll be out getting your own stories, interviewing people, taking pictures, selling ads and real estate listings, and more. Then you'll be back at the computer composing your stories, posting ads, writing editorials, entering real estate listings, and much more.
The bottom line is that you won't need much to start publishing your own newspaper, but you'll need a lot of energy and commitment because publishing a newspaper, even online, requires a lot of hard work. But the rewards are great, and you'll be part of a wonderful tradition to which only a few belong.