The best thing I've found is to carry a small bottle of water with you in the field. When you dig a coin (particularly copper) drop it in the water and put the lid back on. By the end of the day, much of the dirt will have loosened and fallen off. Some of the dirt that remains can be removed by soaking them Olive Oil for a day or two, then lightly brush them with a soft bristled tooth brush. Once the dirt is removed, what you see is the best it will likely be. In other words, as unfortunate as it might be, those pits are there to stay. If it is a key date coin, I don't recommend doing anything. That doesn't mean I wouldn't brush it if it were mine. It just means that I don't advise anyone else to do it to their coins.
I remember shortly after finding my third 1877 IH cent, another forum member found one and sent his in to be professionally cleaned and graded. It was a nice coin that had a layer of green patina. Technically, patina is a form of corrosion. Anyway, he sent it in to have it cleaned and in the process of removing the patina, they toasted his key date IH cent. If not for a couple distinguishing marks, you wouldn't have known it was the same IH cent he'd sent in. So my advice on copper is to soak it and remove the dirt as described above. Then force yourself to leave the rest of it alone. Better off having a naturally attractive coin opposed to a piece of toast. HH Randy