This trick is named because apparently it makes you look like one but I can't quite see it myself.
Without any balls for the moment, let one arm hang straight down by your side. Fold your wrist up so that if you curl your fingers they point to the inside of your forearm. Looking down your arm, turn your hand inwards (turn your right hand anticlockwise & your left clockwise). But keep going, keep your elbow locked & hunch your shoulder forward so that the hand points out to the side. With practise your arm will become more supple & you will be able to turn your hand further round which makes the trick easier. Keep your elbow locked or your hand will naturally curl back round. This is the position your arm is in to make a penguin catch. The ball is thrown up, falls in front of the elbow & lands in the out turned hand.
To throw after a catch you turn your arm back in & throw from the normal position (throwing from the penguin position is possible but also very painful). As the ball lands in a penguin catch unbend your wrist then untwist your arm, then throw the ball bending at the elbow slightly & flicking the wrist up.
Practise throwing one ball back & forth catching it penguin style. It helps to lean the chest forward & push your shoulders forward, this enables you to turn your arms round a little bit further, your hands stick out a bit more so when you actually make the catch your arm doesn't get in the way. Throw to shoulder height & look down on the ball, this way you get to see where the ball is falling, like watching a parachutist dropping out of an aircraft & can position your hand accordingly.
Once you can comfortably catch & throw one ball practise making a single penguin catch in a Cascade. Make all your throws to the same height, pick one ball, as it peaks wait a little longer before you throw the next ball (as the penguin catch is made at a lower point the ball has an increased AIR TIME so you need to add a tiny pause to compensate). When it is time to catch it turn your wrist round into the penguin position. Let it fall into your hand then throw it back into the pattern as normal.
Practise making penguin catches singly, then same ball each time, every left & every right & finally juggling a full penguin cascade. The last one is a 'must have' trick. Remember to hunch your shoulders forward & lean over to look down on the pattern. Keep your arms locked & do all the work with your wrists. Accurate throws are very important. Because your elbows are locked you can't move your arms as much so each ball has to be thrown into the hand.
Also try putting penguin catches into other tricks, full Penguin Mills Mess looks very good as does Penguin Box.