Most packages will install the actual binaries into directories named bin or sbin, e.g. /usr/bin/tcpdump or /sbin/iptables.
On a Debian-based system like Ubuntu, you can use the dpkg tool to display a list of files installed by the package:
dpkg -L vim on my machine produces the following output, for example:
/usr
/usr/share
/usr/share/doc
/usr/share/lintian
/usr/share/lintian/overrides
/usr/share/lintian/overrides/vim
/usr/share/bug
/usr/share/bug/vim
/usr/share/bug/vim/presubj
/usr/bin
/usr/bin/vim.basic
/usr/share/doc/vim
In this case, typing vim from the command line will start the editor. To change which directories are searched, look at the $PATH shell variable. Config files are typically stored in /etc/, or will have example configs stored in /usr/share/ which you can edit and copy to another location.