Packages in Ubuntu have their debugging symbols stored in a separate repo. To download these debugging symbols, run (copy and paste):

printf "deb http://ddebs.ubuntu.com %s main restricted universe multiverse

" $(lsb_release -cs){,-updates,-security,-proposed} | 

 sudo tee -a /etc/apt/sources.list.d/ddebs.list

to add the repo links into /etc/apt/sources.list.d/ddebs.list (This makes it easier to remove the repo). Alternatively, you can also copy each of the deb links into Software Sources and add them from there (Note that you'll likely need to replace $(lsb_release -cs) with the Ubuntu release that you're running).

To download the debugging symbols for package, you can just install package-dbgsym or, in some cases, package-dbg. Note that packages from a PPA don't have debugging symbols available from repos, and that it's the maintainer's responsibility to provide a package that contains the debugging symbols, usually in a package named package-dbg.

Debugging symbols are installed in /usr/lib/debug, although gdb automatically reads in debugging symbols if available and that you don't manually need to specify a location to look in. Depending on the Debhelper Compatibility version of the package, debugging symbols may either be located in a folder with the name of the build ID located inside .build-id (>= 9), or may be located relative to where the executable would be installed (< 9). For example, if you were looking for the location of the debugging symbols for /usr/bin/zip, and the version is less than 9, it would be in /usr/lib/debug/usr/bin/zip.

To remove all debugging symbols and the repo, run sudo apt-get remove .*-dbgsym to remove all -dbgsym packages, and sudo rm /etc/apt/sources.list.d/ddebs.list to remove the debugging symbols repo.