Microsoft has, as promised, released their official Fine Manager for Windows Phone.
The Files app allows you to access all the files stored on your phone. If your phone supports expandable memory with an SD card, like the Lumia 1520, you can use the Files app to access files on the SD card as well. You can browse through files and folders, open and search for files that are on the phone or on SD card storage. You can create new folders and arrange your files across those folders using move and copy functions and you can also rename and delete your files.
In testing the app has is pretty speedy, has a great search feature, and does not require directories to be added ahead of time.
Download the app from the Windows Phone Store here.