I was wondering how to update a page with new stuff like a new news article or something. (The Website is html based). The only thing I could think of is by uploading and replacing the whole .html page with the new article etc. But isn't there an easier way? Like in wordpress where you just sign in and write the article and post it.
What you are looking for is a CMS like wordpress, html is static, so the only way to update it as you said by uploading a new file. In the long run you are better off using Wordpress / a Blog Engine etc. that way the updating becomes seemless.
What is the website and what are you trying to do with it? An alternative is that you can have the articles/blogs hosted somewhere else where you get free WebPress/Bogging like google etc, and in your html site you just put a link to them, and in them you put a link back to your site. That is the least hassle free way of going about it.
Another CMS option that I have heard great things about is http://www.simplecms.com/
You can pull through an RSS feed from some Wordpress blog you setup specifically for your news. There will only need to be minimal effort if you use Google RSS API tools: