This is the opposite of relief prints. 

For etchings, you make grooves in the plate.

Then you force the ink into the grooves and wipe off any ink that's sitting on top.

Dampen your paper and use an etching press to force the paper into the grooves where it gets the ink.

Multiple colors mean multiple plates.

Also in here are two wood engravings. They're really relief prints but the process makes me think more of etchings.