I have an old airport express which I want to use to put a usb printer on my home network and also to extend the wireless reach. I have verizon fios network set up with the router they gave me.
You can use the AirPort Express for sharing a USB printer ... but not to extend the wireless range of yor Verizon-provided router. At least, not by having a wireless connection between them. To share a printer, the Express just needs to be configured to "join" the wireless network provided by the other router. Please check out the following Apple Support article for details.