I am pretty new to Node.js and I went through a tutorial and set up my own server who responses to some requests with basic html.
var body = '<html>'+
'<head>'+
'<meta http-equiv="Content-Type" content="text/html; '+
'charset=UTF-8">'+
'</head>'+
'<body>'+
'<form action="/upload" method="post">'+
'<textarea name="text" rows="20" cols="60"></textarea>'+
'<input type="submit" value="Submit text">'+
'</form>'+
'</body>'+
'</html>';
response.writeHead(200, {"Content-Type": "text/html"});
response.write(body);
I have from a former project (basic html and JS) a javascript function which basically draws a table (calendar).
But how would I use it in Node.js? I dont really understand how I should build up the website?
Your previous code probably depended on accessing the DOM within a web browser. This is not available server side. So you can't generally just use the code you wrote for a client side environment in a server side js environment.
You could look at a library which allows server-side DOM manipulation. See: http://blog.marksoper.net/Server-side-DOM-manipulation-in-Nodejs-with-JSDOM-JQuery-and-Mustache-Templates-April-25-2011.html
If you don't want to write the HTML within your server-code I can strongly recommend Express.js having used it for a year now on my university final year project. http://expressjs.com/
Please note that Express usually expects you to use a templating language for your web-pages such as http://jade-lang.com/. However you don't need to use a templating language. (But they do provide some nice features such as passing JSON into the template)