If I uploaded a file to a website, is it saved somewhere in the Safari application? Or elsewhere in the computer? I scanned a file to my desktop, uploaded it to a website, and then deleted it from my computer. Now this document seems to be gone forever but I need some information from it.

Is there any where it may be stored on my computer? In an application, in a log somewhere. I just need an image of it, I don't need to regain full access to it.
In general, once a Unix file is deleted, it's deleted. That said, there are certain 3rd party utilities that may be able to scour your HD for file signatures that match the file format you used (PDF?) and recover the file. Here is a review of the 3 biggest titles for you to choose from:  http://www.techrepublic.com/article/3-data-recovery-applications-for-os-x/ 

One issue that is critical: Stop using the Mac.  The more you use it and save/alter files, the more likely the disk sectors that contained your scan will get overwritten.