One of the most recognised moves in contact juggling is ‘The Butterfly’. This move is also one of the fundamental building blocks for many other contact juggling maneuvers, so you should eventually be able to perform with no thought involved. The Butterfly was most memorably performed (for me at least) in the 1986 film Labyrinth, starring David Bowie. Although David did not himself perform the contact juggling (instead it was performed by Michael Moschen, one of the pioneers of contact juggling), the film portrays him performing the butterfly and several other moves involving both one clear acryclic ball and multiple balls.
The Butterfly combines both the Cradle and Palm and the Cradle to Cradle Transfer described in earlier posts.
Step 1:
Place the ball in the cradle position, and position your arm infront of your body at about chest height.

Step 2:
In a ‘windscreen wiper’ type motion, begin to toss the ball upwards and away from your body (away to the right if you’re starting on your right hand, and to the left if you started on your left). The aim will eventually have the ball almost seem as if it’s rolling up your hand (hence the ‘contact’ juggling), but in the initial stages of learning, it’s not necessary.

Step 3:
As the ball reaches the top of your hand, and your arm reaches the vertical position, the ball should pass directly over your middle finger.

Step 4:
Once the ball has passed the midway point, contine the arm motion and let the ball fall down the opposite side of your hand, you should be preparing to take any momentum out of the ball at this point, by moving your arm down slightly in sync with the ball.

Step 5:
At this point, the ball should roll into the palm of your hand, and come to rest in the ‘Palm’ position. It may take a bit of practice to get the ball to come to rest nicely after the maneuver, however eventually it will stick!

As stressed with most moves, you should be able to perform this with both hands, in one smooth motion (See why in the next steps!).
Step 6:
Once you’ve reached the palm position, you can then reverse the move and perform the above 5 steps backwards - from the Palm to the Cradle.
Step 7:
Perform the ‘Cradle to Cradle’ maneuver to pass the ball to your other hand.
Step 8:
Repeat the above - using the opposite hand!
The completed Butterfly should be very smooth and the transition between hands should almost be unnoticable. The first six steps can be performed independenty of the Butterfly with good effect, even progressing to passing the ball from one side of your hand to the other, without actually reaching the Cradle or Palm positions. This would mean the ball passes from ‘fingers to fingers’ - which gives you a little less control at first - but should be simple after a little practice.