Open HTML files on Dropbox application
If you try to accessing the files using the regular sharing feature the HTML file will fail to find it's linked CSS, JavaScript, etc files because of the way that Dropbox generates these sharing links.

However you should have a "Public" folder in your Dropbox. If you drop your files in there and select one you should see a "Copy public link..." option above the file list. If you use that, instead of the "Share" button then your HTML file should find it's linked files.