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
To list files currently installed by a package: dpkg --listfiles
To look for new packages: apt-cache search
To find the package containing a given file: apt-file search
To list what can be upgraded: apt list --upgradable
To upgrade only one package: apt-get install --only-upgrade
To upgrade everything: apt-get upgrade