A confident smooth stroke is required in order to have success in any game of pool and billiards. It seems so simple, yet it requires practice, patience and an understanding of how and why it works, or doesn't work.
Parts of a smooth successful stroke are developing the ability to move the cue back and forth in a straight line; understanding that a slight acceleration in your stroke (regardless of how hard you are hitting the cue ball) provides more consistent contact on the cue ball; and we must have the core understanding that the only thing we really control is the cue stick itself. We never touch the cue ball or object balls while playing. This fact helps define the importance of a good stroke.
Parts of a bad stroke are caused by things that we do. The most noticeable is looking up or standing up too quick after you shoot. Another is dropping your back shoulder which allows the front of the cue (Your tip) to wander in space on the way to and through the cue ball. Another is jabbing or poking at the cue ball with your cue.
When trying to cure these common mistakes give these ideas a try. Don't move at the end of your stroke until the balls have stopped moving. This helps keep your entire body still and helps focus on the follow through.
It is critical that your back shoulder does not move during your practice strokes or your follow through. Try to look at it this way. Your elbow is a one way joint. Take advantage of it. Any twisting comes from your wrist or shoulder. Look at your arm from your elbow to the grip like it's a pendulum. When you back stroke the pendulum has swung back. When you stroke and follow through the cue ball the pendulum has swung forward. If this motion combined does not form an arc like a pendulum then you are dropping your shoulder. You will notice also that executing this correctly causes the tip of your cue to move down towards the table when you follow through.
What you want to do is have a smooth acceleration when stroking the cue ball. I am going to borrow a tip I received from Jerry Breiseth in the 1970's. Picture a 2 foot length of large rope, 1 inch in diameter and hold it on one end. If you throw this rope with a quick jerking motion, it will not go very far. If you threw the rope with a smooth swing back and accelerate forward, the rope can go a long ways. Try to picture that natural acceleration when you swing the rope. This feeling is what you want to develop in your stroke of your cue. As your stroke improves you will be thrilled with your improved consistency in shot making and cue ball control. I hope these hints help you get in stroke!