Squat down on the mat with your hands on the floor shoulder width apart and your elbows bent to get into position for the most basic tumbling move -- the forward roll. Tuck your head and dip forward. Touch the top or back of you head to the mat as you start to roll over. Round your neck and back completely so each part touches the mat easily and not squarely. Generate more momentum as your practice your rolls and you will eventually learn to come up on your feet.
Gain a feel for the backward roll, also known as the reverse somersault, by rocking back and forth on the mat with a rounded neck and back. Get into a front roll position and rock backward until your neck touches the mat. Bend your elbows and place your hands on the mat with your fingers pointing toward your shoulders, and then rock forward into a standing position. Once you are flexible enough to get your hands flat on the mat in proper position, push through the backward roll with your arms. Roll straight back over your head, not to one side or the other.
Walk up into the handstand position by crouching a short distance from a wall with your back to the wall. Slowly kick one foot, and then the other out to the wall. Walk up the wall with your feet to get into a handstand position. Move your hands closer to the wall to get into a more vertical position as your feet move up the wall. As you get more comfortable in the handstand position, push your feet off the wall and hold your position without any support. Keep your back straight and prevent your hips from bending by tightening your stomach muscles.
Once you are able to hold a tall, strong, steady handstand position without support, master the cartwheel -- a vertical move through the handstand position. Facing forward turn your left foot out. Turn your head left. Lunge forward and place your left hand on the mat pointing out. Kick up your right leg to generate momentum. Place your right hand down, pointing out, about shoulder width from your left hand. Plant your right foot pointing back. Plant your left leg and you come to a standing positioning looking back towards the direction you came. Reverse the process to do cartwheels the other way.