They're using diving bells that are very LARGE versions of a diving bell. And they have created a sort of hose that connects the bell to the surface. Beneath the bell they begin to open up the ground and use a composite of materials that is combined with wood to be sealed water tight and in affect create a tunnel under the giant bell that is effectively water proof. The resource they are mining underwater i'd rather keep secret and only give that knowledge to character who would be privy to it. Some steam technology can be seen, but nothing more than that.