Usually you would want to access the items in the Places menu located to the right of Applications in the top left corner of the screen.
The "Computer" option will give you a view of the removable storage devices on your computer (CD drive, USB drives, etc.) as well as the file system. To get a view of the complete file system go to Places > Computer > File System. This should open a window titles "/ - File Browser" with the full contents of your main file system, which is generally the contents of your hard drive.
For your personal documents and other user files, you can open the "Home Folder" bookmark (usually right at the top of the Places menu) or one of the other bookmarks in that first section.
All of the icons in the first two sections of the Places menu will open the file system explorer in Ubuntu which is called Nautilus although the window will likely be titled "File Browser".