Using Debian Lenny
I want to start using Aptitude.
I have been reading through the manual and articles, but have
some questions.
Is upgrade the same as safe-upgrade and dist-upgrade the same as
full-upgrade?
When would I use safe or full upgrade?

According to the manual it says:
When would there be a need for this? Would it be necessary in
a stable release?

When should I use purge. wouldn't I want to remove the config files if
I am removing the program?

I cannot answer all your questions as I am not familiar with full-upgrade, however, I can tell you the regular upgrade will upgrade installed software to newer versions available in the repository, dist-upgrade will upgrade you to the newest version of the OS, say for instance Lenny is superceeded by sid in the stable branch a dist-upgrade would upgrade everything, of course I usually use apt-get for specific packages, but I also like aptitude which is a front end for apt-getin a curses based front end.

As far as purge goes, you may want to remove configs unless you are reinstalling it later or adding a new version.

Incorrect and misleading.

'upgrade' is the old name for 'safe-upgrade' and will update packages without adding or removing any packages. Sometimes, new versions depend on new packages, or packages are removed, etc. 'dist-upgrade' is the old name for 'full-upgrade' and will upgrade everything that needs upgrading, removing packages or adding new packages if needed.

Not quite right; aptitude is another frontend for dpkg. It's also been Recommended over apt-get by Debian for years. And it's not just curses-based; most of the command-line commands are the same as in apt-get.

I found this in the Aptitude user's manual:
I'm not understanding how this would be a problem. Wouldn't Aptitude upgrade within
the same release?

Thanks

Yes. You will not move releases unless you change your sources.list, or your sources.list e.g. points to "stable" instead of "lenny" and the definition of "stable" changes to "squeeze" (when squeeze is declared stable).

You seem to be missing the key point here. As explained before, the big difference between the regular upgrade and dist-upgrade/full upgrade is that the latter will remove packages in addition to updating and installing. If, for example, there's a conflict that requires removing a library that kde, or gnome, or xorg, or whatever depends on, then say goodbye to your kde, gnome, or xorg (and everything that depends on them).

dist-upgrade is mostly there for the purpose of upgrading to a new distribution level, where the main idea is to configure the base system to the specified point. Higher-level user tools take a back seat to this. Yes, it can be also used within a single release and usually not be too much of a problem, because the base system won't change too much, but you do have to watch what it does very carefully, because it will sometimes attempt to remove things you don't want it to.