In diaboloing 'Cradles' are tricks where you weave the string into patterns around the diabolo. Here's how to make a the most common cats cradle using the handsticks. Visually the result is the same as with Cats Cradle, the finger method.
Spin the diabolo & do a little Chinese Whipping to get as much speed up as you can. Swing the diabolo as if to do an Around the world with a stopover moving the stick you are swinging under forward so that the string gets caught & begins to wrap around the stick. Instead of catching the diabolo on the string, cross your other arm underneath the forward handstick. Allow the diabolo to just hang in a loop from the forward stick. The loop that is holding the diabolo should form a triangle. Keeping the forward handstick still thread the tip of the other handstick through the triangle from the outside. That is if you swung to the left, thread the right handstick through the triangle from the left to the right.
Now raise both handsticks so that they point straight up & gently pull them apart until the string is tight. If all has gone well the string should form an underlined cross. To exit just turn the handsticks in towards each other & tip the loops of string off of the ends into the middle.
For the complete cats cradle experience, you need to flick the diabolo from the bottom string & catch it on the top of the cross. So form the cradle again just as you did before, then keeping the sticks as flat as you can, quickly pull the sticks apart to throw the diabolo up into the air, this will also tighten the cradle. Point both sticks straight up & catch the falling diabolo on the top, cushion its fall so that it doesn't bounce around. Again to exit tip the handsticks inwards.
Also try catching the diabolo inside one of the triangles formed by the length of the handstick & the crossing string. It's a pretty tight catch if you use a short length of string. Also note that if you try to exit with the diabolo caught in a triangle by letting go the diabolo will just fall to the floor. You can either throw the diabolo back out of the triangle or make a quick Recapture.
After learning the cats cradle you might like to try the trick's big brother - Tigers Cradle.