--- search package name
apt-cache search emacs
--- install one package
apt-get install emacs23-nox
--- preparing upgrade (fetch and index latest versions of the repos)
apt-get update 
--- actually update one package
apt-get upgrade myslice
--- list packages
dpkg -l
dpkg -l '*foo*'
--- list (files for) one package 
dpkg -L myslice
dpkg-deb -c myslice_0.2.4.lxc.2013.11.26_amd64.deb
--- detailed info (e.g. to see complete version that is truncated in dpkg -l)
dpkg -s myslice
dpkg --info -c myslice_0.2.4.lxc.2013.11.26_amd64.deb

--- install from a local .deb 
dpkg -i foo.deb
- or, if this has deps that need to be pulled through apt-get:
gdebi foo.deb
(install with apt-get install -y gdebi-core)

--- find which package a file belongs to
apt-file search /path/to/file
(can be installed with : sudo apt-get install apt-file)