Very good questions and I also would like to know more.
Since I have seen a lot of old concept arts for sprite graphics (e.g. Donkey Kong:
http://www.mariowiki.com/File:Jumpmanconcept.jpg ) that might mean people in those times used less computers. Well of course the computers were used when writing the game itself. But I mean during the design process everything was done with just a paper and a pen.
The computers they used must have been like some old Commodore computers were (probably much older than the famous C64). They didn't have any advanced graphical user interfaces and simple command lines were used a lot. I believe the coders had some sort of specifications or utilities to make programming easier but I'm not sure what exactly they were like.