Probably should ask the instructor. (Also BTW, this thread probably should have been posted in the beginners forum.) The steps you post are apparently for a very specific regular grid terrain rendering algorithm supporting LOD, which they call quadtree. Haven’t read that book, but bunches of such algorithms are possible.
Not that I see it in those steps you posted, but just from the name my guess the terrain tessellation alg (i.e. how they bust up the terrain into triangles) they’re describing mimics quadtree subdivision. That is, you take a big grid of heightposts, bust it up 2X2. The vertices touched by those cuts form your lowest LOD. Bust each of those 4 squares up 2x2 and that forms your next lowest LOD. etc. on down to the resolution of the grid.
Please don’t quote me though; read the book. And if they don’t explain it well, toss it and get a better book.
Since it sounds like you’re just starting out with graphics programming, forget the terrain for starters. Start by drawing a single triangle using immediate mode (glBegin/glVertex/glEnd) with no lighting (glDisable( GL_LIGHTING )). Once you get it rendering on screen, draw another triangle. using the same technique right beside it sharing an edge. Then switch to drawing these same two triangles using one glDrawElements call for both.
Once you’re to that point, then plug in the terrain alg. All it’s probably going to give you is a new set of triangles to render, besides the two you have been.