While all the things that were said on the previous page about how to hold a ukulele may make sense to you, and while you may be able to hold onto it while you're not doing anything particularily complicated or demanding with either of your hands, I've come up with a couple of simple exercises to help your brain and your hands instinctively understand how to do their job once things start getting into motion. You don't want to be thinking about gravity when you should be thinking about music.
The first exercise simply involves letting go of the ukulele with both hands. "Look, ma, no hands!" Click the "play" button to see me letting go with both hands, somehow magically keeping the ukulele right where it is, and then easily putting my hands back in the playing position, without the ukulele falling to the floor like it did the first dozen times I tried it. Note that I've "flipped" the video, so you can treat it like you are looking in a mirror.
Once you can do this, over and over, comfortably, without dropping the uke, you will have begun to cultivate a certain "instinct" to keep the uke where it needs to be, without depending on your hands, which will be busy with other tasks.
The next exercise will help you develop the brain and muscle reflexes you need to hang onto that uke when your right forearm/wrist is busy. Yes, a lot of people lead happy and productive lives playing ukulele without ever even trying exercises like these. They develop the same skill through years of playing songs, and having little moments when the uke seems more interested in the Earth's gravitational field than it does the person playing it. What we hope to accomplish is to get you some of those holding skills, that they can begin to be second-nature when you begin fingering chord shapes and strumming - which you are going to have to deal with on the next page!
In this exercise, the strumming hand and arm abandon the ukulele completely, leaving it completely in the hand that usually does the chords. Yikes! The trick here is to be able to instantaneously return the uke to the playing position with just the one hand, and to get the strumming hand back in business without any mussing or fussing that would certiainly interfere with whatever it is you are playing.
Try these exercises a few times. It's best if you can get quite comfortable with them - but even if they just leave your mind and body with an impression of what is to be expected of them, you will have a point of reference to work towards as you focus on strumming, and don't want to waste your mental energy and focus on just keeping the ukulele there where you need it.