If you are the normal UK club tennis player, then the volley is a must for your game, as in the UK doubles becomes the normal club game. It is a shame that this is so, and in some respects this move towards doubles play in clubs and leagues has taken away the singles part of tennis. I know that many players feel they are either too old for singles or not fit enough, but out here in Spain the league system is still built on singles even at the veteran level. Anyway back to the volley...The basic forehand and backhand volley should be made with a short, blocking motion. Keep your swing compact and use the power of your opponent's ball against him or her. Normally, you will not have time to turn your shoulder and hips like you would on the ground strokes. Simply put, your racket must be prepared.

Preparation
Using a Continental grip, lay your wrist back and prepare the racket head for contact with the ball. Keep your elbow and racket head in front of your body as you move to the ball. Too often I see students use a back-swing to prepare. You should avoid taking your racket back behind you with your elbow away from your body. On the backhand volley let the non racket hand assist in drawing the racket back, and so also helping the shoulders to turn.

But lets get into some more detail, and I will start with the backhand high volley, which seems to cause the most problems.
Backhand volleys are difficult to learn and master. One of the contributing elements of difficulty is what I call the bent elbow syndrome'. That is, when a player turns for the backhand volley, the natural tendency is for the elbow to bend.

The problem with players who have not mastered the volley is that they tend to straighten the elbow to make contact. If you look at most all skilled players, during the backswing, (or well before contact), the hitting arm locks firm and straight. (Observe the backhand volley of Pat rafter below and you will see this feature among almost all skilled players.)

I won't get into the physics of why this is important. What I will say is that when players bend the elbow, they tend to swing too big for one thing; they also lose power and control due to having to control the aspect of the elbow in addition to the other stroke components. Players who learn to maintain a conscious and firm elbow position from start to finish on the backhand volley gain mastery of the shot faster and with more effective volleys.

Here is a simple analogy.
Imagine your racket is a mirror. If the ball were a beam of light, it would reflect downward at an angle similar to it's incoming angle. (The angle of incidence of a beam of light is equal to the angle of reflection off a mirror.) Gravity will increase the downward angle that the ball rebounds off the flat racket face as well. One additional element that affects the angle of reflection:
An incoming ball with underspin will rebound downward at a steeper angle off a flat racket face than a ball that is incoming with topspin.

This helps explain why so many people bury even reasonably easy volleys that are well above the net into the bottom of the net! Players often fail to comprehend these rebound characteristics of a ball off a flat racket face.

Also look at this photo of one of the great volleyer's, Pete Sampras.Look at his set up, as he moves to the ball he makes the space, and you can see he has his elbow away from his body, and his non racket arm is behind his body, so keeping the shoulders from rotating ( as in the 3rd photo of Rafter )

And the pic of Justin Henin here  shows the arm position as really straight on contact.One very important point to mention is "not to brake".

Many players are taught to stop and plant their front foot just before making contact with a volley. This might be OK in a lesson, but in a real match you have to move forward quickly to intercept your opponent’s passing shot. If you check your forward momentum by stopping on your front foot, you run the risk of netting your volley.
Why?
Just like when a car stops too quickly, running toward your volleys and stopping abruptly causes you to tilt from the waist, which, in turn, causes your racket face to close slightly. That may be just enough to send your volley into the net. Instead of braking before you hit your volleys, do what the pros do and continue to move through your shot. Not only will that keep you from dumping the ball into the net, it will also add a little extra punch to the ball.

Enjoyment
Learn to enjoy this much ignored and neglected stroke. There is nothing better than getting to the net and finishing the point with a winning volley.
To improve this shot you just have to get up there and try it.

A nice clip of the backhand volley of the great Pete Sampras - note: shoulder turn, short take back, straight arm on contact, and the movement through the stroke.

And here is his forehand volley!