Read the release notes! This can't be emphasized enough. The Debian developers are careful to include all the important details on what has changed between releases, and any special steps required prior to and after the upgrade process.
There are two ways to handle a major upgrade: all-at-once, and a little at a time (which we'll refer to as a partial upgrade). The all-at-once upgrade basically involves a single command that updates all packages. The partial upgrade method involves selecting a group of packages and updating them and their dependencies. This reduces the dependency calculations to a more easily handled subset. Generally, one selects one of the meta packages, such as GNOME or Apache2, or a selected set of packages to update, and uses the install command in either apt-get or aptitude, or selects the packages in dselect, aptitude, or Synaptic. After they are upgraded, the next set is chosen and updated, until all packages have been updated, along with any new dependencies or removals required. At some point, after the majority of software has been upgraded, the remainder of the upgrade can be handled all at once.
Choosing a subset of packages is fairly simple. The apt-get dist-upgrade command and aptitude full-upgrade command will provide information on what will be added, upgraded, and removed and ask you to confirm the selection. At this point, you can tell them not to perform the upgrade, then review the packages proposed for upgrading, and select one or a few to use with the apt-get or aptitude command line install command (which upgrades already installed packages). A similar procedure works with Synaptic.
One way to ease the upgrade process is to perform a standard package upgrade first. This will perform the simpler, standard package upgrades that don't require major changes in dependencies. Once this is done, the full distribution upgrade will involve fewer packages
