I tried to find proper services for generating PDF files in Liferay, however I have found only class PDFProcessorUtil. How to use it to generate PDF file? How to save the generated file then? I think I should use
DLAppLocalServiceUtil.addFileEntry to save file into Liferay storage.
Liferay's PDF-conversion works by converting documents in the document library and offering them for download - this is implemented through Open Office. Install Open Office or Libre Office, run it in server mode and configure Liferay to use it, then you can choose to select downloads as PDF. The HTML format has a few limitations, as it can include so many external resources, so I'm not sure what your result will be.
If you're generating the HTML output yourself, you might want to consider any other (Liferay-independent) means of generating PDF, as you might not need to upload your files to the Document Library (e.g. if you're generating reports on the fly and just want the generator result to be PDF, but not store them). If this is what you need, you can use any pdf converter library you want - Liferay does not limit you in your choice.