I think this is not a Reader problem, as the free Reader cannot produce PDF files. In InDesign, I would go to File > Print > Print as PDF. I would suggest contacting your printer for the settings to use. Even better if you are not experienced in this, ask him to produce the PDF.
You can also use File>Export and export to a PDF from InDesign but as Claudio mentioned, you would want to find out what settings the printer wants. Typically the Print preset in InDesign is god enough.
Or you could use the Package feature in InDesign to package all of the needed files up and send all of that to the printer (assuming they have InDesign.)