This is just my list of common commands for apt and dpkg, Debian's software package management system.
The list of locations that packages are loaded from is in /etc/apt/sources.list
Refresh the list of available packages
apt-get update
Search for a package
apt-cache search searchtext
Install a package
apt-get install pkg
Uninstall a package
apt-get remove pkg
Upgrade all installed packages
apt-get upgrade
Upgrade the kernel and base packages
apt-get dist-upgrade
Install a package that was downloaded as .deb file
dpkg -i file.deb
Reconfigure a package (if you missed a question when you first installed it)
dpkg-reconfigure pkg
Find which package a file belongs to
dpkg -S /path/file
List all the installed packages (that's the lower-case letter L, not a one)
dpkg -l
Find an installed package with regex on the name (those are backquotes)
dpkg -l `regex`
See exactly what files are in a package
dpkg -L pkg
See exactly what files are in a .deb file
dpkg -c file.deb
See metadata for a .deb file
dpkg -I file.deb