To work on PDFs in your SharePoint repository on SharePoint on-premise with a web browser, you just need to log on to your SharePoint web portal, navigate to a PDF and click it. You will be prompted whether to check out and open the PDF. See also Check Out and Open. Then you can check in to save it back to your SharePoint repository.
Tip: If you need to save to your local folder, after editing the PDF you can click File > Save As > Computer and choose a local folder to save.