1) a 2D engine with clever graphics that make it look 3D (the most common)
2) A 3D engine with a locked camera position (more common on consoles than PCs)
3) A hybrid of the two.
I recommend this page for a good description of Isometric engines, and how to write them: http://www2.aros.net/~npawn/tuts/isointro.html
You can also find a lot of links to (and pictures of) isometric engines on this page: http://www.multimania.com/hatti/MrY/isoxeng.html