Both salinity and temperature affect density, although in different ways. Density differences are what make some water sink and other water rise. You can take it from there.
At this epoch, the main source of deep water is a small area in the vicinity of Norwegian Sea, where the surface water is very cold, and high winds evaporate enough surface water to make the salinity high. Hence the surface water is unusually dense, and some of it sinks, creating a source for a north-to-south slow current in the deep waters of the North Atlantic. A secondary source of deep water is in the Weddell Sea adjacent to Antarctica, and the reason for the sinking there is similar; a further minor source is the Ross Sea, on the Pacific side of Antarctica. The "Antarctic Bottom Water" formed in the Weddell Sea is so dense that it is believed to flow UNDERNEATH the southbound water that came from the vicinity of Iceland. But both of these masses then crawl eastward into the Indian and Pacific Oceans, where their "signature" is evident from their low oxygen content (because it has been a long time since they were at the sea surface).