Look up what a “cofferdam” is. They basically put a watertight fence around the area where the pillar will go, then drain all the water out. Now you have a dry area in the middle of the water where you can build a pillar as you would on land. Once the pillar is built, you pump water back in and remove the cofferdam.
It depends on the exact depths you’re working at. Oil & gas extraction, especially in the relatively shallow North Sea, developed a lot of solutions for these kinds of things.
First step is you need the bit that’s actually under the sea floor, the foundations. These are usually piles – long bits of steel or (rarely) concrete going into the sea floor. These tend to be assembled on the surface then lowered to the sea floor and hammered into the sea bed with hydraulic hammers. This is mostly a remote process but some assistance is likely to be needed from divers, usually saturation divers.
From there you need a “pile cap”, which ties all the piles together to act as a single structure, and then you start building your pier or tower up toward the surface. These elements are usually concrete. It might be possible to install formwork underwater and use an underwater-curing concrete. Or it may be necessary to install a cofferdam of some kind and work in the dry, but at elevated pressures, near the sea floor. Having humans working at pressure in cofferdams can be a very risky business.
Norway is going a different route.
At Bjørnafjord in Western Norway the water is half a kilometre deep which is far too deep for a conventional bridge; so they are going to build a bridge whose piers float on the water and are held in place by cables attached to the bottom of the fjord.
[https://dissingweitling.com/en/project/bjørnafjorden](https://dissingweitling.com/en/project/bjørnafjorden)
This is just part of a colossal infrastructure project to upgrade the E39 route along the coast which currently requires a large number of ferry journeys. The B1M has a video about this plan which is the sort of thing you can only do if you have all the money in the World:
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