They put on their scuba gear and climb into a vessel that shaped like a torpedo and not much bigger than a shower. Powered by a single rear propeller, it deploys from the host submarine. After hours of slow, calculated movement through water too shallow for any submarine, radar indicates the SEALs have reached shore. Still underwater, they slide back the top canopy of their vessel and swim the last stretch to the beach under cover of night.
The key tool here is the SEAL Delivery Vehicle (SDV), the modern version of what's essentially a tube with a propeller stuck on the back. It can be as compact as needed, sized to fit just one Navy SEAL or as many as six. These craft are typically "free-flooding" vessels, which means they're filled with water. The soldiers inside breathe through their own scuba tanks or from on-board oxygen reservoirs. The first guys to lock themselves inside these coffin-sized machines were Chuck Yeager-grade brave.
The idea of a scaled-down, maneuverable submarine has been around for decades. Full-sized subs can't operate properly in water shallower than 50 feet, so getting covert forces from ship to shore is tricky. Going in with scuba gear may require more oxygen than can be contained in a normal tank, and swimming in flippers for that long can leave even a hardened SEAL too exhausted to perform the mission.