Nexus 7 doesn't support storage over USB OTG only. For that, root your nexus 7 and install "stickmount" (root app on playstore) that will allow you to mount usb drives.
Otherwise you can use any usb peripheral (mouse, keyboard, joystick, etc) out of the box.
Oh, and update your nexus 7 to 4.1.2 asap. It fixes a storage bug that exists in 4.1.1.
Basically if you filled your nexus 7's storage past 3GB free space, the apps and the OS would start stuttering. Turns out TRIM was disabled...4.1.2 enables it again (only for the nexus 7 with samsung emmc). If you are experiencing stuttering, update to 4.1.2 then use the app "Forever Gone." The app will fix any past TRIM errors by completely filling the free space with blank files and then deleting it.