Generally speaking you have two options.
-with cruise ships which visit South Georgia often on the way to Antarctica
-with private yachts offering South Georgia as a special destination in their program
For me it was very clear, that I would go for the yachts, as I wanted to stay on South Georgia more than the 2 to 3 days the cruise ship are offering. I onyl can recommend this option for everybody who wants to photograph professional or semiprofessional or who is just a bit more adventurous. Depending on the yacht you can stay 3 to 4 weeks on South Georgia, that will give you enough time to do lots of photography on this island.
the passage from the Falkland Islands takes depending on the yacht about 5 days, the returning to the Falklands, head on against the prevailing winds, takes even longer, at least 6 days. Thats the price you must be ready to pay. 5 to 6 days on the roaring fourties, so second a peaceful moment where you do not have to cling to the boat with all legs and arms you have, storms, drifting ice of various sizes and for the most of the passengers sea sickness.
Around South Georgia everything is more relaxed, as there are enough safe anchorages.
I sailed with the Sarah W. Vorwerk .
The yacht offers a high degree of comfort and enough space for big equipments. Henk and Jaqueline are experienced sailers, who have been sailing for many years in these latitudes.