This upgrade from lenny to squeeze is not more complexer then the update from etch to lenny.
If you read everything carefully your server will run after upgrade too:)
Before you go on please read the official Debian release notes:
Recording your session:
script -t 2>~/upgrade-squeezestep.time -a ~/upgrade-squeezestep.script
First you should update your running system:
aptitude update && aptitude dist-upgrade
Check the package state:
It will show any packages which have a status of Half-Installed or Failed-Config, and those with any error status.
If you had a kernel upgrade please reboot. After successfully updates replace the sources from lenny to squeeze: