Pull-ups work every muscle in your back. FInd a horizontal bar at about head height. Monkey bars are ideal. Grasp the bar with an overhand grip, hands slightly wider than shoulder-width apart, and sink down below the bar until your arms are fully extended. Use your legs to help push your body up through a pull-up, then use as much arm and back strength--and as little leg strength--as possible to control your descent. Once you're strong enough, aim for a full set of 12 pull-ups without any help from your legs. Just bend your knees to keep your feet from hitting the ground as you pull up and lower yourself down.
Push-ups work your chest and arms. Place both hands on the bottom edge of a playground slide to elevate your upper body, then walk your feet back until your body is straight from head to heels. Lower your chest down toward the slide, then push your chest back up. As you get stronger, you can progress to doing push-ups with both hands and feet on the ground, then with your feet up on the slide and your hands on the ground.
Leg dips work your thighs and glutes. Place one foot on the bottom of the jungle gym slide, facing up the slide. Let your other foot dangle off the edge of the slide as you squat down, sticking your hips out behind you. Stop just before your rear foot contacts the ground, then use your front leg to power yourself back up to a standing position. As you gain confidence and strength, you can turn this into a plyometric exercise. Every time you straighten up make the movement into an explosive jump, switching feet while you're in the air and using your new front leg to slow and stop your downward momentum before your back foot touches the ground.
Knee-ups work your hip flexors but, more importantly, your abs must work to keep your body from swinging as you move your knees. Hang from the monkey bars or any other convenient pull-up bar. Squeeze your abs tight and bring your knees up in front of you, trying to keep your body still from the hips up. Lower your legs and straighten them, ending with your feet slightly forward of the line of your upper body. Repeat. As you get stronger, you can lift first one leg at a time, then both legs together, straight out in front of you instead of bringing your knees up.