How do I download a package from apt-get without installing it?

There are a least these apt-get extension packages that can help:

apt-offline - offline apt package manager
apt-zip - Update a non-networked computer using apt and removable media

This is specifically for the case of wanting to download where you have network access but to install on another machine where you do not.

Otherwise, the --download-only option to apt-get is your friend:

 -d, --download-only
     Download only; package files are only retrieved, not unpacked or installed.
     Configuration Item: APT::Get::Download-Only.

Try

apt-get -d install <packages>

It is documented in man apt-get.

Just for clarification; the downloaded packages are located in the apt package cache at

/var/cache/apt/archives