The side handstand straddle-down is a trick that was in the old J.O. women's Level 6 beam routine, and even though it's not required in the current cycle of compulsory routines, it's still a good trick to have under your belt.
Most gymnasts choose to start out this trick by doing a cartwheel into a side handstand. This is an essential part of the trick, and is also part of the current Level 5 and 6 beam dismounts. Getting control of the handstand here is achieved by developing strong arm, shoulder, back, and stomach muscles. Sound like a lot for just a handstand? Well, think about it. The arms and shoulders are what hold you up in a handstand, and make the tiny adjustments for balance. Your back and stomach muscles are required to hold your body in a tight alignment. If you were loose in your midsection, the lower part of your body (i.e. your legs and hips) could waver back and forth, and would pull you over on one side or the other.
Refer to the arms and shoulders conditioning page for a few exercises that will help develop arm muscles, and the abdominal muscles conditioning page for exercises targeting the stomach muscles. In addition, practicing to hold handstands on the floor, against the wall, and on the beam are also very good exercises for developing the proper upper-body muscles.
Once you can consistently hold side handstands on the beam, you need to learn how to fall over backwards. What in the world does that have to do with straddle-downs, you ask? Well, in order to have the correct balance to press down, you need to have your shoulders slightly beyond the 90-degrees perpendicular with the beam. Practice holding the handstand straight at 90-degrees for a few seconds, then push your shoulders over the beam without arching until you fall over backwards. (When you fall over this way, it's a good idea to twist out of it so you don't land blindly.)
Now you can start trying to straddle down. The movement is the exact opposite of pressing up to a handstand, and it should be just as slow. You should have complete control of the descent the whole time. Once you have straddled and have begun to press down to the beam, lean your shoulders over the side of the beam so that your center of gravity remains centered with the beam. Your legs are on one side of the beam's plane, so you have to lean your shoulders over to compensate.
Keep pushing with your arms so that your feet land lightly on the beam. This entire trick is a slow one, and when this was in the old Level 6 routine, the judges took off two or three tenths of a point for lack of control.
This is definitely a trick that requires lots of practice, so keep at it, and good luck!