See how it's done
The first thing you want to do is make sure you have a good stance. If you are kicking with your right foot, you want to be facing angled slightly to the right of where you want the shot to go, thus you should be running from the left side of the ball. If you are 'left-footed', you'll be doing the opposite. If you are taking this shot as a free kick, make sure to give yourself about three steps to get to the ball - more than that can cause you to overshoot your target.
The idea is to kick the ball with the very bottom of your big toe (where the toe meets the foot), striking the ball on the bottom corner (right foot = bottom right corner). Assuming you do this correctly, the amount of bend put on the ball depends on two things: the motion of your kick swing and the power of the kick.
As you plant your back foot before the kick, you want to make sure that you are still facing slightly wide of your target. Don't let your planted foot spin as you swing your kicking leg. Try to kick from your hip and use your upper leg to generate the power, always kicking through the ball. Upon striking the ball, begin to curve the swinging leg in the direction that you want the ball to curve. As you do this, curve your foot slightly in the same direction and the ball will roll a little further up your foot. Your leg will follow a sort of arcing path toward goal. Follow through is very important here: concentrate on your fore-swing all the way through the ball and you might just score. Watch the video linked above to see the motion in slow motion.
The power with which you kick the ball and the amount of spin that is generated are inversely related. In other words, the ball will go straighter the harder you kick it. Chipping the shot will produce much more bend than a bullet shot will. Begin by kicking the ball with a very casual swing, concentrating on foot placement above all else. Once you have that down you can alter the speed of the kick as necessary.