To uninstall a package, keeping configuration files:
apt-get remove <packageName>
To uninstall a package and associated configuration files:
apt-get remove --purge <packageName>
To remove orphaned packages:
apt-get autoremove
To check state of a given package:
dpkg -s <packageName>
To download a package without installing it:
aptitude download <packageName>
To extract contents of a package, use the ar command (binutils package):
ar x <packageFileName>
To search for a package:
apt-cache search <regex>
Some reference information: