I remember being amazed as a kid when my elder brother used to place a coin on the end of his elbow then swing his hand down to snatch it out of the air before it had a chance to fall. In this trick you catch one ball on the underside of your forearm near the elbow just where you'd put the coin.
People with muscular forearms will find this trick much easier to learn than bony people & using squishy underfilled beanbags rather than using solid balls will be a big help too.
First things first - despite the name you don't actually catch the ball on the tip of your elbow. Point your arm straight out in front of you then bend it back so that your hand is beside your ear. Turn your hand so that your palm is facing downwards, when holding a ball in this position many people tend to turn the palm upwards which in turn causes the arm to tilt to the side slightly which can make the ball roll off the arm. Look straight down the underside of your forearm, first notice that your elbow right at the end is pretty narrow. You don't want to catch the ball here because even if the ball doesn't simply bounce off the hard bone it is more likely to roll off the side. Moving up the forearm towards the hand your arm will get wider then narrower at the wrist. Ideally you want to aim to catch the ball at the widest point of your forearm, this will typically be the most muscly bit & the softer muscle will help cushion the fall of the ball & once cushioned the ball will have further to roll off.
Flex your bicep while bending your arm as far as you can, you should be able to notice a shallow groove appear between your muscles. It won't be much but it is better than nothing! Basically, aim to catch the ball in this groove at the widest point of your forearm.
Take one ball & throw it straight up in front of you to just over the height of your elbow. Bring your elbow underneath the ball & cushion the fall with your shoulder while keeping the underside of your forearm as flat as possible. Keep practising until solid.
From a cascade catch a ball & immediately carry it to beside your head then throw the next ball up to your elbow & catch it. It is that simple, but will require a lot of practice.
You could just throw the ball off of your elbow back into a pattern but there are more interesting ways to exit from this catch. You could obviously throw the ball held in your hand beside your head & Claw the ball as it falls off of your elbow just like in the coin trick. Quickly extending your arm round the outside of the ball & making an Elbow catch also looks really nice. Or if you're feeling clever you could roll the ball up your forearm into your hand.