The quick answer: very expensively! The step-by-step answer would be: first, dig a trench on the ocean floor. Then, drop sections of giant concrete tubing into the trench. Seal these sections tightly together to make them waterproof, and to make a really long tube. Pump all the water out. Cover everything up again with ocean floor. Voila, a brand new tunnel!
Another way to do this is to use a boring machine. They aren’t ‘boring’ at all, and actually quite cool! Also known as TBMs or ‘moles’, they look like huge cylinders with a flat face called a ‘cutting wheel’, full of sharp discs, which rotates and breaks into the rock. They can be designed to bore smoothly into all kinds of ground, and can go under cities as well as under water.
Answered by Carlos Grau