Many of the people who did not drown immediately during the sinking of the ship died in the water as a result of hypothermia - the water temperature was below freezing. Many of the lifeboats refused to row back to pick up survivors from the water, even though they had space, fearing that they would be swamped by the number of people trying to climb aboard. Some of the survivors were able to cling to the underside of an upturned lifeboat and paddle to safety - still, only half of them survived the wait for rescue (Jack Phillips, the radio operator, was among those who died).
It was at 4am - almost two hours after the final sinking of the Titanic - that the first rescue ship, the RMS Carpathia, arrived to pick up survivors. It took several more hours to get everybody on board.
Above, a boat from the ship MacKay-Bennett (a cable-laying ship chartered by the White Star Line as part of the search effort after the disaster) examines an overturned lifeboat from the Titanic.