What's the easiest way to build down into water?

Water is notoriously difficult to remove in Terraria, placing blocks over it will not work as you have already tested. Here are the few methods I know of from personal experience:

• For small pools, buckets are a simple but tedious method of transporting the water elsewhere.
• Large pools can be drained into below caves or sent directly down to The Underworld where it will form obsidian on contact with lava and/or evaporate.
• There are other ways to remove water by utilising exploits and bugs but for the sake of avoiding cheats, I won't list them here.

Alternatively, you could keep a small amount of water in your base for use as a crafting station or fishing spot. I suggest the easiest solution would be to use a hellevator to easily drain water into The Underworld.

On the other hand, if you'd like to construct a building inside a large pool of water, you can use either of the previous methods to great effect by building up your walls to hold back the water you'd like to keep before draining the interior.

Actually, I did a test and I did find a way to "remove" water from where you want to build.

In my case, I created a platform over the water, and then I filled rock in as far as I could reach. Now, typically if you dig out the rock, your new, empty space will fill back up with water.

However, after creating the blocked, rock region, I stopped the iOS app and restarted it. After the restart, the rock seemed to exist without any other settings persisting that would force that area where the rock was residing to contain water. So, I dug out the rock, leaving only the sides holding back the water, and no water remained in the enclosure.

I guess this is using a bug/exploit, but it is allowing me to build through water. It's not perfect, but it does work.

The easiest way, in my opinion, is to simply dig a shaft out the bottom of the water until you run into a cave, and let the water drain into the cave.