dpkg does the installing; apt-get manages depencendies and pulls things down from repositories.
To install a .deb file:
dpkg -i foo.deb
To list installed packages:
dpkg --list [pattern] # pattern is something like 'wine*'
To report the status of a package:
dpkg --status <package-name>
To list files currently installed by a package:
dpkg --listfiles <package-name>
To look for new packages:
apt-cache search <search-string>
To get details about a package:
apt-cache showpkg <package-name>
To find the package containing a given file:
apt-file search <filename>
To list what can be upgraded:
apt list --upgradable
To upgrade only one package:
apt-get install --only-upgrade <package>
To upgrade everything:
apt-get upgrade