Pruning Rose of Sharon questions are quite common. The good news is that it is such a low maintenance plant that in most cases, it really doesn't need to be trimmed to stay healthy and vibrant in your garden. Most people see the "Rose" in the name and assume it needs the same level of care. It normally doesn't. However, there are some things you can do if it looks like it needs it.
One thing that people sometimes don't realize is that this plant can grow to be quite large. Twelve feet is not uncommon. Sometimes you'll need to prune just to keep the size in check so it doesn't overcrowd the rest of your garden. You'll want 6 to eight feet of clearance to other plants.
If you are trying to train it to be a tree, then you'll need to trim the side shoots from the "trunk" as well.
You can cut it back quite a bit, even more than the traditional 1/3 rule you'll find with most roses. You'll want to leave a good two to three feet of canes there though, or at least a couple of buds. Use variety of lengths on the cuts so your plant doesn't look like it got a "buzz cut"! You can use a lopper or hedge trimmer but its best to use some shears to give it a more bushlike appearance.
The best time to do this is in the late spring while it is still dormant. Cutting before the buds open will help new growth and add additional blooms in late summer, when it starts to flower.