We know today that all it takes to have a day-night cycle is a rotating earth and light coming from one direction. The Bible tells us clearly that God created light on the first day, as well as the earth. Thus we can deduce that the earth was already rotating in space relative to the light-source.
God can, of course, create light without a secondary source. We are told that in the new heavens and earth there will be no need for sun or moon (Revelation 21:23). In Genesis, God even defines a day and a night in terms of light or its absence.
The evidence that ordinary days are being referred to is so overwhelming that even liberal Hebrew scholars admit that the author of Genesis could not have had any other intent—particularly when the words ‘evening’ and ‘morning’ are used from the first day. (See The Answers Book Chapter 8, and CSF tract Six Days? Honestly!)
On the fourth day the present system was instituted as the earth’s light-bearers were made, so the temporary light source from the first day was no longer needed.