jsPDF can't get any styling to work

I think the problem is that you use media="print" instead of media="screen". Try making two seperate files, one for print and one for the screen:

<link rel="stylesheet" href="print.css" type="text/css" media="print"/>
<link rel="stylesheet" href="screen.css" type="text/css" media="screen"/>

The screen one will contain the styling for the page as seen in a browser. The print one will contain the styling for when you print your page, or in this case saving it as a PDF.

EDIT

I checked the jsPDF website but I think they don't support CSS. You could do something like this to create a document with different text colors though:

doc.setFontSize(22);
doc.setTextColor(255, 0, 0);
doc.text(20, 20, 'This is a title');

doc.setFontSize(16);
doc.setTextColor(0, 255, 0);
doc.text(20, 30, 'This is some normal sized text underneath.');

Put this code right under var doc = new jsPDF('landscape'); in your script.

you can try this option, that uses jsPDF, html2canvas and html2pdf libraries

from its README:

include this files:

<script src="jspdf.min.js"></script>
<script src="html2canvas.min.js"></script>
<script src="html2pdf.js"></script>

and then you can generate your pdf by running:

html2pdf($('body').get(0), {
   margin:       1,
   filename:     'myfile.pdf',
   image:        { type: 'jpeg', quality: 0.98 },
   html2canvas:  { dpi: 192, letterRendering: true },
   jsPDF:        { unit: 'in', format: 'letter', orientation: 'portrait' }
});

You can capture a screenshot with jsPDF, but you'll need html2canvas as well. Use html2canvas to convert the html to canvas and grab the image content. Create an empty pdf with jsPDF and add the html image content into the pdf and save:

html2canvas(*html*, {
  onrendered: function(canvas) {
    const contentDataURL = canvas.toDataURL('image/png')
    let pdf = new jsPDF()
    pdf.addImage(contentDataURL, 'JPEG', 20, 20)
    pdf.save('form.pdf')
  }
})

This will retain all CSS but the quality will suffer a little (blurry).