In order to have enough dry land to build the city, workers were conscripted to level hills and fill in lakes. Those swamps/marshes were drained and filled in. Seawalls and canals were also built to help mitigate flooding (which as you will read, was not so successful). Additionally, I think we can look at the fortress first built, the St. Peter & Paul Fortress, which employed sinking large wooden piles into the ground for support (as they did at Venice). No doubt this method of strengthening the foundation soil was employed where the ground still was too weak to bear the weight of the buildings above. (This method of using piles to increase max bearing capacity is still used today, more often in concrete form).

And, it is important to note that building something and successfully building something are two different things. They didn't escape the water and the city suffered quite frequently from flooding (over 300 floods on record since city founding in 1703)(1). I mean, there are sections of the city as low as 4 feet above sea level. The most recent major flood occurred in 1975 and resulted in 111 inches above sea level, or 9.5 ft (5 ft of water!). The have since built a dam that hopefully will extremely reduce the risk of this flooding...

I also think you might enjoy reading this very short, (and slightly biased) article from the Cambridge Sentinel on the city of St. Petersburg, written in 1912.

It Is said that moisture underlying the city can be seen sometimes oozing up between the paving blocks on the Nevaky Prospect, a busy thoroughfare. The city is not only built over water, which often threatens to Inundate it, but It Is visited by rain and snow at least two hundred days of the year. The city Is practically surrounded by water, for swamps abound on two sides, the sea and the river on the other. At the beginning of the building St Petersburg, Peter the Great set thousands to work, "under compulsion of the knout," to build dikes and reclaim the land.

Long story short, inevitably thousands conscripted to build the city died, the environment suffered some massive abuse, and a city was built but unable to resist frequent and sometimes devastating destruction thanks to floods.

Resources:

Mapping St. Petersburg: Imperial Text and Cityshape By Julie A. Buckler

D. V. Ryabchuk et al.. The Neva Bay (Russia) – antropogenic lagoon. All-Russia Research Geological Institute.

Interesting article on St. Petes Paris of the North or City of Bones