How do I install zlib on Debian 6?

sudo apt install zlib1g

Possibly

sudo apt install zlib1g-dev

as well.

A zlib command does not exist:

$ dpkg -L zlib1g
/.
/usr
/usr/share
/usr/share/doc
/usr/share/doc/zlib1g
/usr/share/doc/zlib1g/copyright
/usr/share/doc/zlib1g/changelog.Debian.gz
/usr/share/doc/zlib1g/changelog.gz
/usr/lib
/usr/lib/libz.so.1.2.3.3
/usr/lib/libz.so.1

It is a library.

If you are searching for anything use apt-cache search.

And if you need a command to compress use either gzip or zip.