You can use the adb command which comes in the tools dir of the SDK:
adb shell
It will give you a command line prompt where you can browse and access the filesystem. Or you can extract the files you want:
adb pull /sdcard/the_file_you_want.txt
Also, if you use eclipse with the ADT, there’s a view to browse the file system (Window->Show View->Other… and choose Android->File Explorer)