First and MOST IMPORTANTLY, I located the breaker switch for my oven and turned it off. I verified this by noticing that the electric clock on the oven display was no longer powered.
After removing all the oven racks, I removed the two screws at the bottom of the back end of the oven holding the metal "floor" in place.
Removing the "floor" cover exposed the old heating element and I was able to quickly identify the corrosion of the old heating element which caused it break.
I unscrewed the two screws attaching the heating element to the bottom of the oven, then there was another screw attaching the back of the heating element to the back wall of the oven.
I had to pull the element towards me with a decent amount of force. This is the "quick and dirty" way of getting the job done, because I didn't want to have to find a way to pull my entire oven out from the wall of my kitchen in order to gain access to the back panel. Eventually with enough pulling, the two wires came through the holes with the gator clips still attached to the element (good! it would not have been fun if one of those came off too soon). Incidentally, a bit of fiberglass insulation also came through the holes. It didn't seem to be a big deal, I just discarded the fluff.
I detached the gator clips from the old heating element and removed it. It had a fair amount of black carbon residue (I assume) so you might want to wear gloves for this part or at least have a paper towel handy to clean your hands up.
Just follow the same directions in reverse the get the new element in. Hook up the gator clips, shove them through the two holes in the back of the oven, remount all the screws, remount the oven "flooring" and screw it back in. Before replacing the flooring, you may want to try turning on your oven to ensure it gives a nice pretty orange glow. Of course don't forget to let it cool down before proceeding, if you do that!
Don't think you have to be an expert to do this one. I was able to diagnose and fix this problem without any prior oven repair situations under my belt.