Roughly a day and a half to two days each way by ship, so about four days of a sailed itinerary go to the crossing. A fast southbound run sometimes buys you a bonus landing at the other end. If you fly across instead, it's a flight of about two hours each way.
That four day figure is the one to hold onto when you're comparing itineraries. A 10 day sailed voyage gives you closer to four or five days on site, with the Drake either side. It's the single most common thing people get wrong when they compare trip lengths on price alone.
The crossing time isn't dead time, though. Lectures, biosecurity briefings, and seabird watching all happen out there, and the ship's naturalists are usually on deck with you.