How do I properly install Steam on Ubuntu 16.04 LTS?

You nearly had it correct, to install steam you need to add the -i flag to dpkg like this:

sudo dpkg -i steam_latest.deb

And if that still fails you can install python-apt this way, which you as well had almost right:

sudo apt-get install python-apt

As you are trying to install Steam, here is a different approach: Install Steam directly from Ubuntu's multiverse repository

sudo add-apt-repository multiverse
sudo apt-get update
sudo apt-get install steam