I would first suggest a kneaded eraser, if you don't use one already.
A kneaded eraser can be shaped like putty. This means you can form points, lines, and a variety of other erasing surfaces with it. This allows you to easily erase just the place you want.
Additionally, it doesn't erase the same way as your rubber or Mars plastic (polymer) erasers, which leave bits behind and may wear down you paper. It actually lifts up your graphite or charcoal marks. This means you don't have to brush or blow the residue away.
This property also allows you to only partially erase something. For instance, you may have placed a large swath of grey that's a couple shades too dark. You can pat at the dark area to lighten it, instead of erasing it and starting over.
I have tried and own eraser shields, but they don't work very well with erasers that have lost their edges. When I do use them, it's with my kneaded erasers and not my polymer erasers. In that case, they work very well as stencils for the point you knead.
As for the points, you need to roll them thick and shallow instead of thin and steep, in order to have enough strength in the tip to hold up. I generally just make a ball, pinch part, and make a cone out of it.
Unless you want to erase very finely, such as adding highlights to hair. In that case, you can leave the point long and thin, and it will gently lift up fine lines of pencil.
Once you start using kneaded erasers, you'll find that they're really an entirely new implement, quite unlike regular erasers. Since you can adjust the amount you erase by changing pressure and eraser shape and even the way you apply pressure (standard erasing motion, patting, rolling, stippling!), you can get very fine control over what you're doing.
And you don't have to worry about erasing holes in your paper!
Now, to be fair, kneaded erasers have downsides. The harder your lead (4H and up), the less effective I find these. Likewise, the harder you press with your pencil, the less effective they are, because they can't pick up the graphite dust.
If the kneaded eraser won't do it, use a polymer eraser (I throw out rubber erasers). You can always use a craft knife to "sharpen" them into a point or chisel. Sharpening polymer erasers makes them work much better with eraser shields, too!