dpkg -i <package.deb> Installs a package file; one that you downloaded manually, for example.
dpkg -c <package.deb> Lists the contents of <package.deb> a .deb file.
dpkg -I <package.deb> Extracts package information from <package.deb> a .deb file.
dpkg -r <package> Removes an installed package named <package>
dpkg -P <package> Purges an installed package named <package>. The difference between remove and purge is that while remove only deletes data and executables, purge also deletes all configuration files in addition.
dpkg -L <package> Gives a listing of all the files installed by <package>. See also dpkg -c for checking the contents of a .deb file.
dpkg -s <package> Shows information on the installed package <package>. See also apt-cache show for viewing package information in the Debian archive and dpkg -I for viewing package information extracted from a .deb file.
dpkg-reconfigure <package> Reconfigures an installed package
man dpkg Will give you more info on these commands as well as many that are in less common usage.