When you hit a forehand your non-hitting hand has to get out of the way of the tennis ball and your racket as you swing forward and rotate back toward the net. You have a lot of leeway when it comes to where your non-hitting hand can go during your forehand motion.
So how, exactly, can you get your non-hitting arm out of the way? Some players, such as myself, simply bring their hand over. Some players bring their non-hitting hand up higher so they can catch the racket. Andre Agassi would sometimes hit and then his non-hitting hand would explode upward with his body as he followed through, and Pete Sampras would just leave his hand up there.
What you want to make sure that you’re not doing is getting your other arm out of the way in a manner that interferes with your shoulder rotation. Some players swing their other arm out of the way, causing their shoulders to open up too early. This makes them catch the tennis ball late or in an awkward position. The way to correct this problem is to focus on your shoulder rotation as you swing to contact. It’s not really possible to leave your non-hitting arm out in front of you if you rotate your shoulders correctly. By focusing on your shoulder rotation, your other arm will largely take care of itself and get out of the way without interfering with your technique.
Let’s look at some pictures of Andy Roddick to see how he varies the movement and location of his non-hitting hand. In this first picture, Andy has his other arm down by his waist as the tennis racket is up around his shoulder. In the next shot, the racket is again up by his shoulder but his non-hitting hand is now also at shoulder level, similar to Pete Sampras. So, again to reiterate, Andy has a number of different things he does with his non-hitting hand depending on the particulars of each forehand, but his other arm never interferes with the other mechanics of his shot, particularly rotating his shoulders back toward the net as he swings.