I have to go to bed now so I can't give a good in depth answer. But I don't want to leave you without a great source I came across a couple months ago. The basic facts are that there was fertile land and valuable peat under the water. When there is money to be made humans find a way. For the Netherlands "the way" was the creation of modern pumping, excavation and dredging technologies.

From Hand-drag to Jumbo: A Millennium of Dredging warning PDF. Start on page 8 for the Netherlands.

Be careful though dredging is an addictive topic. It all starts with a couple pages here and there and the next thing you know you're spending sleepless nights pouring over reports from the building of the Panama Canal.

I can't really help you with this question, but I can point you to an essay about Venice that resonates with your question somewhat. Venetians obviously faced some substantial flooding-based problems as well. Elizabeth Crouzet-Pavan takes an interesting approach to Venice's water problems in her essay "Toward an Ecological Understanding of the Myth of Venice."

It might be worth reading. It's only like 15 pages and you can find it in Venice Reconsidered, edited by John Martin and Dennis Romano. PM me if you want more details.

Depends on the region, and your definition of 'advanced engineering'. From the northern coasts up to what's now southern Denmark (roughly the inland areas of the Wadden Sea), where floods were a more immediate threat, since about 500 BCE settlements were built on large artificial hills as a place of refuge. These are called 'wierde' (or the local dialectal equivalent) or 'terp', from the old Frisian word for village.

Mind you, these artificial hills could over be 5 meters high (the tallest is almost 9 meters) and were large enough to hold small villages. Their builders might not have had access to 'technologically advanced engineering', but they were definitely capable enough to make the area habitable, as did their later successors.

For the Netherlands, there was initially less flooding, because the land was higher. Simple drains worked, then sometime in the Middle Ages, simple drains, with a swinging door at the mouth of them that closed off the drains from the river at high tide. As it was worked, drained, and farmed, the land subsided and the simple door ceased to be enough. So then polders were built, then higher polders, then windmill-powered drain pumps, etc. So, you could say that, once people had started living there, they kept doing things that made it more flooded and also did things so they could continue to live there. They didn't walk in from the east, see a flooded landscape, and wonder how they could change it so they could move there.

Taming the Waterwolf: Hydraulic Engineering and Water Management in the Netherlands during the Middle Ages William H. TeBrake

Technology and Culture Vol. 43, No. 3, (Jul., 2002), pp. 475-499