Here's the thing. My windows computer is giving my a hard time getting to use my OS and my files stored. I am planning on install Ubuntu 14.04 on a USB Flash and then I will try to get access to my files so that I can copy them over to an external HDD. Will this work? If not, can another method be suggested to me? Thanks for the support.
Yes it should work. When you boot into the live usb, open disks (press windows key and type in 'disks'), select the hard drive you are talking about and click mount.
Then you will be able to access the files with the file manager (called 'files').
The external hard drive should automount so you shouldn't have any trouble with that.