The most important thing is to let the white of the paper work in your favor - don't try to cover everything with charcoal. It seems obvious, but a lot of people think charcoal drawing means filling every area, and then you just end up with that lifeless gray smudge. The trick is to establish your dark points clearly defined from the start, mark where you want to keep the paper white, and only then blend the midtones between those contrasts. If you've already started too dark everywhere, it's pretty much impossible to get that visual impact back.
Now, something nobody's mentioned yet: try using a real eraser before blending, not after. Get a kneaded eraser - those pink or black ones - and mold it into a really fine point. After you draw, you're removing charcoal with precision in areas where you want more brightness, creating strong contrasts before you blend. It's like sculpting light into the drawing. After that, when you blend, you're working with a foundation that's already well structured, with clear and dark areas well defined.
The blending stump itself is fine, but I'd recommend using it with a really light touch and small circular motions, not those long strokes that just spread everything around. And yeah, fixative between layers helps a lot - you can add more charcoal on top without compromising what you've already done. That gives you total control over the final result.