I backup my site's database with NAS storage, but now that I need to get some of the files, I realize I don't know how to download them to my desktop. Is there a way to download from FTP or straight from the terminal, or? I have the NAS storage mounted on my linux machine (centos).
If you have the NAS mounted, it really isn't any different (in this case) than the rest of your files. You can just copy them.
Without more information (specifically, how you are doing the backup) it is difficult to craft a sensible response.
In general, for a granular restore like this, what you want to do is:
1- restore (to a DIFFERENT LOCATION) the smallest piece you can that contains all of what you need to access. Generally, you will restore using whatever tool was used for the backup.
2- Backup the information you are about to be change in the event you screw up. Back it up to a different location than the (old) backup from which you are restoring!
3- Access the restored information however necessary (i.e. Outlook if it is a PST file) and do the import, replace, etc. into the primary system.
4- Clean up