The city came to rest upon the planet's icy crust, denting it under its immense weight, but not touching the surface. It would remain suspended on ice until it was removed and the city lowered to the planet's dry surface many months later.
When Atlantis first landed on the planet, the first thing it did was to release a pre-cursor wave of mining nanites into the ice beneath the city. Those nanites worked their way down to the bedrock, forming small tunnels and transit conduits back to the city in the process. When the nanites eventually reached deposits of neutronium, naquada, and other valuable minerals they transported tiny pieces backup through the conduits and into the city's collection terminals.
With the assembled raw materials from Hoth, as well as other small offworld mining sites, the first building constructed by Atlantis was a Terra, quickly built by the specialized factories within Atlantis designed to create identical ground bases on each world the city landed on. In order to expedite this process, Atlantis was constructed with a hollow center beneath the city. It was from this niche and the adjacent factories that Hoth's Terra was quickly built, and now functions as the center of operations on the planet, as well as retaining itself as a landing pad for any future visits by Atlantis or another city-ship.
Hoth's infrastructure snowballed as more raw materials were collected, allowing more mining nanites to be created and more replicators producted to speed up construction of the planet's infrastructure. Before Atlantis left the planet, over 100 buildings were added to the circumference around the Terra, including a small shipyard for the construction of Navicula Porta and a Pesqua factory.
After leaving, Hoth remained connected to the growing Alterran/Lantean Pegasus infrastructure by means of two stargates left on the planet. One is the standard Pegasus variety, while the other is a traditional orange cargo-transfer gate used to ship the varying natural resources collected to offworld factories en mass without interfering with normal gate travel.
Currently Hoth supports over 500 structures and a living staff of 16 Lanteans and one Alterran(Kyle Stevenson). A secondary shipyard has been constructed to facilitate repair/construction of midsized vessels.