My across the street neighbor has a beautifully placed weeping Japanese maple in their front yard. It is the showpiece of their landscape, but I knew it needed a bit of grooming, so I volunteered. First, the tree is about 10 years old and has never had much done to it. One of the good things about this tree is that it does not have limbs that touch the ground (if it did, they would begin to spread along the ground). If this were the case, I would remove the ones on the ground back to another branch that was not touching the ground.
The first thing I did with this tree, as I always do, was to go all over the tree and remove any dead wood, even small twigs. I literally break any limbs off that would not require a lopper or a saw to remove (this tree did not have any limbs that large). Once all the dead wood is removed, I always examine any that were broken off, and make a clean cut where they broke.
Once the dead is removed, I start looking for crossed branches or branches that are rubbing, and remove them. Now this is what is different about pruning these trees. Instead of keeping the vigorous stems, remove them, and keep the weaker stems. This helps the tree to maintain a better shape.
Now that you have removed dead wood and crossed branches, stop, stand back, and look at the tree. Now comes the hard part. Does it look the way you like it? If it is poorly shaped or lopsided, then you need to evaluate several thing before you make another cut (remember this is a slow growing tree). Look at the sun and see if the plant is poorly shaped because one part of the plant is getting more sun than another part. If that is the case, prune the sun side to encourage the shadier side. If sun is not the issue, have someone shake each limb you think you want to remove, and imagine the plant without that limb. If it looks ok, and does not destroy the shape you want, then remove it. If you want to remove several large limbs, do it over a period of several years. If all is good, then the only other pruning I might do is to remove some small branches to encourage light getting into the tree promoting more growth in thin areas of the tree. In the case of these maples, I practice under pruning versus over pruning.