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if I know html can I build my website without paying anyone and publish it.
You can create your own content, but you would still need hosting and a domain. There are free options to both, but both are generally cheap for good quality. Hosting ranges from 5-20 dollars a month and a domain is around 10 dollars a month.
There are also options like GitHub Pages - https://pages.github.com/ - where you can host your website for free.
To answer your question, you are correct. You can get a website up and running without paying anyone! Hope that encourages you even more to continue with the plunge! Keep learning!
Treehouse offers discounted hosting for students http://webhostingforstudents.com