Since a .deb package contains files, you would think there would be a way to list the files within the package. Well, you would be right; just use the -L option:

# dpkg -L xsnow
/.
/usr
/usr/doc
/usr/doc/xsnow
/usr/doc/xsnow/copyright
/usr/doc/xsnow/readme.gz
/usr/doc/xsnow/changelog.Debian.gz
/usr/X11R6
/usr/X11R6/bin
/usr/X11R6/bin/xsnow
/usr/X11R6/man
/usr/X11R6/man/man6
/usr/X11R6/man/man6/xsnow.6.gz

To go the other way around, and find which package contains a specific file, use the -S option:

# dpkg -S /usr/doc/xsnow/copyright
xsnow: /usr/doc/xsnow/copyright

The name of the package is listed just to the left of the colon.