Search for a CMS (Content Management System). Joomla, for example, is free and widely used. There are others also. But probably, you'll need support from the IT dept to install it on the school's server and help you with configuring it. And that will cost them time, so you'll what's called "management commitment" (the school management team saying "That's a good idea!" and freeing some resources for the implementation).
There's a lot of blog software also. And what's a blog other than kind of a electronic paper?
And maybe, the school is planning to implement MOSS (Microsoft Office Sharepoint Server). That could be made to fit your requirements also.
If your school currently has educational software like Blackboard (widely used, but maybe not on high schools), that's kind of a CMS also. So you might be able to make a "Breaking news" section there, that's accessible to all concerned.
What all these options have in common: you don't need any knowledge of HTML!
Kees
Hi! I was hoping that someone could help me out:
I am part of a High School Newspaper that comes out biweekly. Limitations on the staff and commitment prohibit us from coming out more frequently so we miss a lot of breaking news. I was hoping that there was a way for me to create a website that allows me to have it running at all times and allows the writers to upload the stories instead of a web admin to the page. I know ive seen it before. The problem is that I dont know HTML... so if anyone has anything like this already built, ill buy it for a reasonable price.

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