Kick serves change direction on the bounce. Breaks right for a righty, left for a lefty. Aka American Twist serve.
You basically hit it the same as a topspin serve, but get around the side of the ball a little more. If you're right handed, think of a standard topspin serve as hitting from 6 to 12 o'clock if you can imagine a clock face on the back of the ball. A kick serve should be 7 to 1 or further over. You should be able to hit this with the same toss as your topspin serve.
Also, I disagree with this graphic:
Really, you should be able to hit every serve from the topspin/slice serve position. For kick or topspin, just move the ball toss closer to the baseline (less in front). This makes it impossible for your opponent to read your serve based on your toss.