Basically, when I went to try and upload a file using my Samsung Galaxy Note 10.1 and clicked on the Moodle File picker windows, Upload a file Choose file button, my only options available were Camera, Camcorder, Sound Recorder, Choose Music, Dropbox, Gallery, Music player, Photos, and Samsung Link. It took me a few minutes to realize there was no file manager option, which is the default when doing the same thing from a desktop computer.
I went to the Android Play Store and searched for free file managers, and literally just picked the first one in the list, File Manager by Rhythm Software. After that I was able to upload any type of file I wanted to, and I was also able to search through all the tablets folders.
I have installed the same file manager on my seven inch Samsung tablet and my Samsung S4 phone. Works like a champ on all three devices.
By the way, I tried uploading with the supplied Android file manager that came on my 7 inch tablet...would not upload the file to the file picker, but the Rhythm Software file manager fixed it right up.
This file manager coupled with Kingsoft Office, and all of the PoodLL add-ons, makes it possible to do an awful lot of fun stuff from a tablet, and turn them in as Moodle assignments.