The second step of the tennis backhand volley is the forward swing to contact. Once you have pivoted and gotten the tennis racket into the proper position with the racket head behind your hitting hand, you swing forward by simultaneously stepping forward into the court by stepping forward with your inside foot and transferring your weight to that foot. At the same time, swing forward with your racket and your arm to your contact point, which will be out in front of your body. The key to swinging to contact on the volley is that the arm and racket swing forward to the tennis ball by driving forward together as a unit from the shoulder.
The forward swing to contact on a backhand volley is a little bit different than your forward swing on a forehand volley. Essentially, there is more of a downward component to the swing path on the backhand volley. You are still swinging forward, but the greater downward swing angle of the backhand volley will create more backspin on the tennis ball. There are some noticeable similarities here with a slice backhand. As you swing forward to the ball, your non-hitting arm (your back arm) should extend out behind your body (moving the opposite direction of your hitting hand). This will keep your shoulders turned sideways and help you stay balanced.
Just like on a forehand volley, you will have a very short follow through. The tennis racket stops much sooner on a volley than it does on a backhand groundstroke. It’s probably a bad idea to focus on the follow through of your backhand volley at this point. Instead, make sure you are driving the racket and arm forward from the shoulder as a unit and let the follow through take care of itself.
At 1:25 in the video we can see Frank swinging to contact on his backhand volley. He steps into the court with his inside foot, transfers his weight to that foot, and turns his shoulders sideways. At the same time, he swings forward by driving the racket and his arm forward from the shoulder as a unit. He makes contact with the tennis ball out in front of his body, and he keeps his non-hitting arm back for balance. He has a very short follow through after making contact. You can also see that there is a downward component to the swing path on his backhand volley, and this downward component is going to put backspin on the tennis ball.