From the Estancia Cerro Paine, take the trail that leads first south, then west up the Rio Ascencio valley to the base camp used by the Italians in 1963 during their first ascent of the South Tower. From here one must shuttle loads up the valley past the linga trees, and then up a giant moraine to the glacial lake below and to the east of the Towers. Hike up a snow gully to the left of the cliffs at the head of the lake. A long and sometimes steep slog up the glacier leads to campsites on top of a 900' rock outcropping below the East Face of the South Tower.
This route follows a stunning, gorgous line up the South Tower. It was climbed by the Canadians Sean Easton and Conny Amelunxen in 2000 after 24 days including 19 nights in a portaledge. It consists of 27 pitches ( 1100 meters ) of climbing up to 5.10+, A4 with ice climbing of WI 2 -3. More information can be found in the American Alpine Journal 2000, pages 272 - 275.
I can't say from personal experience on this route but my judging from the route we attempted, my recommendation would be a full A4 rack of pins from rurps to 1 1/2" angles, hooks, copperheads, many nuts and many camming devices. If fixing lines always bring some sort of sheaths or padding to keep the ever present Patagonian winds from sawing your ropes in two over edges!
If I could have gone back to do a climb on the South Tower, this would be the line I would have liked to ascend.