It's not very hard to do - but it can take a while to get the hang of it. The trick is to overpower your forward cast. Really jam that line forward hard & then stop the cast very quickly, all of a sudden. This causes the leader to tuck under the line. Your fly then comes crashing straight down to the water, as if it has fallen from the sky. This allows your fly to sink down deeper a lot faster. Its a cast to use in situations where the sooner you get the fly to the bottom, the better.
The first time I performed the tuck cast it was by accident. I was casting into a fairly stiff breeze that day, foolishly. On one cast the wind let up just as I was trying to punch my forward cast through. I realized this & stopped the cast very quickly. The result was a beautiful tuck cast - even though that wasn't what I was trying to do!! After realizing what had happened I tried to recreate this cast. It took me a while, because at first it feels wrong (at least to me it did). Casting, so I thought, was always supposed to be smooth & graceful. Indeed, the tuck cast is, but it took me a while before I got the feel of the abrupt stop to the cast.
The best way to explain the tuck cast is to show it. The short video below is an excellent demonstration & explanation of the tuck cast. If you fish below the surface, this is a great cast to have under your belt. It will help you pick up more fish when you need to use it. The best part is that it's an easy cast to learn.