There is a fantastic movie about the breeding/brooding/hatching cycle of the emperor penguin, which came out in 2005. The March of the Penguins.
For a clip, see https://www.youtube.com/watch?v=L7tWNwhSocE.
According to the March of the Penguins reference cited above, the males incubate the eggs and the females, who have gone to the sea to feed, feed the chicks when they (the females) return.
The penguins practice serial monogamy within each breeding season. The
female lays a single egg, and the co-operation of the parents is
needed if the chick is to survive. After the female lays the egg, she
transfers it to the feet of the waiting male with minimal exposure to
the elements, as the intense cold could kill the developing embryo.
The male tends to the egg when the female returns to the sea, now even
farther away, both in order to feed herself and to obtain extra food
for feeding her chick when she returns. She has not eaten in two
months and by the time she leaves the hatching area, she will have
lost a third of her body weight.
For an additional two months, the males huddle together for warmth,
and incubate their eggs. They endure temperatures approaching −62 °C
(−80 °F), and their only source of water is snow that falls on the
breeding ground. When the chicks hatch, the males have only a small
meal to feed them, and if the female does not return, they must
abandon their chick and return to the sea to feed themselves. By the
time they return, they have lost half their weight and have not eaten
for four months. The chicks are also at risk from predatory birds such
as northern giant petrels.
Addendum requested by OP:
Except for station personnel, most people wanting to see Emperor penguins or other Antarctica wildlife fly to the tip of South America or to New Zealand and take a ship from there. SA is the departure point for the Antarctic Peninsula and the Weddell Sea. NZ is the departure point for the Ross Sea area.