As far as I have seen, just redoing your upgrade should finish/correct the failed operation. I don't ever recall a situation on my debian box where the system was ruined from apt-get and not reverasble by just correcting the fails and really running. As far as the options, they really are pretty simple.
Update works on updating the repository list of available applications.
Upgrade will upgrade all packages to have new versions available unless a situation happens where a upgrade would cause a break in the dependencies.
Dist-upgrade does about the same as upgrade however is also including the kernel and many lower level system updates made to the os.
Clean "cleans" the junk that may be left from upgrades installs and removals. If I recall it asks before cleaning some files.
Autoclean does above w/o asking.
Hope that helps!
As far as I recall that's about as easy as it gets, debian is one awesome distribution and is a great platform to work with.
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