Wirelessly browse your Mac's files from your iOS device

Teaser: 
It's a common enough scenario. Your chock-full-of-files Mac is in the downstairs office. You're flat-backed on the couch upstairs with your iPad. There's a file on that Mac that you'd dearly love on your iPad but the idea of trudging downstairs to retrieve it makes you tired. What to do?
Christopher Breen
Wireless, iOS, Networking, Wireless, Utility software, App Store, iOS 6