Marching Cubes algorithm help

Hey! I just want to know something about marching cubes which I am a little confused about.
So you know how you use the lookup table to look up where the triangle connects. Number one do I have to create those points on the edges of my cube? Number two what about the iso surface and what do I do if it changes, do I have to create those points or vertices on the edge too? What about the four main vertices. I know they are like switches but do they actually connect to anything? Do those four points need to be vertices or just points with data. Thanks!

All done and dusted. This was alot simpler then I thought. Though adding ‘nice’ looking noise is tricky I’ve managed to add… ok looking noise haha. Either way thanks for anyone who took the time to read!