Wikipedia has a good article on it, including photos of what the marks look like. They're practically invisible to the naked eye, getting them to show up usually requires additional steps like taking high quality scans and running them through some color filters, or using a UV light.
From the EFF coverage of it, it sounds like every laser printer probably prints these marks now. I'm not sure if inkjets or other printer types do or not.
They probably started with the inkjets. More so, considering that inkjets have turned into a money grabbing scam. You're better off with a laser printer if you need only B&W.
From the wiki they mention researchers created a tool to check the identification code yourself, or to anonymize documents you're printing: https://github.com/dfd-tud/deda
Clearly a pain in the ass and not user friendly for the general public though.