(1) "Out-of-the-box" with stock system software without any modification, using Media Importer App from Play Store, you can view/play files/video etc. stored on a MicroSD card (copied via a PC), but you can't write files to the card (when connected to Nexus). You have to use a PC to write files to the card.
See FAQ of the app: http://nexususb.blogspot.com/2012/08/faq.html
(2) Root the system, install Stick Mount or USB OTG Helper from Play Store, you can read/write MicroSD card using this reader, copy files between device's internal storage and the card -- like what you normally do on a PC.