Before you start throwing balls, cross your arms with the right hand on top. Now move your arms so that the left hand is on top. Then move back to right on top. Continue this for a while to get the feel of what your arms will be doing. This way when you start throwing balls, you'll have one less thing to think about.
Now practice throwing two balls. Start with your arms crossed, right hand over left. One ball should be in your right hand and one in the left. Toss the first ball from your right hand backwards toward the right side of your body. As soon as you make that throw, uncross your arms and throw the ball in your left hand straight up. Your hands should continue to recross with the left on top. As they cross, catch the first ball thrown with your left hand and catch the other ball under your arm with your right hand. Practice starting with your left hand on top too.
Now add a third ball. Do the same thing I described above, but do a little exchange at the very end. Practice it in both directions.
The next step is to combine the two moves you've been practicing. That last little exchange under my arm in the last step isn't really part of Mills Mess. That's just a good way to stop the pattern at that point so that you can learn it in small parts. This is a good time to go back to the top of the page and look at the whole trick again. Notice that two of the balls follow each other in a sort of figure eight pattern on top. The other ball just goes back and forth on the bottom.
Now look at the last video on this page. See how the top hand ends up with one ball in it? As soon as that top hand catches that ball, immediately throw the ball back toward the other side of your body. It will be the same throw you did as the very first throw, except from the opposite hand and in the opposite direction. From there, you do the same things you did the first time, but all in the opposite direction. Remember that every time your hands cross, you need to throw the the ball in the top hand back across your body and uncross and recross your hands again. Concentrate on getting the top two balls doing the correct thing and hopefully the bottom ball will take care of itself.