Getting stuck in is to fully commit oneself (mentally, physically, emotionally, and spiritually) to a cause of great meaning; be utterly committed and determined to reaching your objective. If a person is fully stuck in, nothing can stop them from reaching success. It is a very respectful term that can be voiced to those you love in order for them to have good luck/fortune.
Person 1: I'm off to write a math test.
Person 2: Get stuck in lad.
Person 1: Thanks man I'll try my best.
A phrase describing something so incredibly confusing that you have no idea how to get through it. Comes from the Water Temple in Zelda 64, one of the most insane levels I've seen in any video game, ever. No joke - EVERYONE gets stuck in the Water Temple when they play this game, usually for weeks/months/years.
"What am I supposed to do next?! GAH! This is like being stuck in the Water Temple!!!"