The southern supercontinent Gondwana (Gondwanaland) included most of the landmasses which make up today's continents of the southern hemisphere, including Antarctica, South America, Africa, Madagascar, India, Australia-New Guinea, New Zealand, and New Caledonia. (The remaining continents at that time—North America and Europe-Asia—were also joined, forming the northern supercontinent, Laurasia.)
Although Gondwanaland was centered roughly where Antarctica is today (at the extreme south of the globe), the climate was generally mild. Global average temperatures were considerably warmer during the Mesozoic than they are today. Gondwanaland was then host to a huge variety of flora and fauna for many millions of years.
The supercontinent began to break up in the late Jurassic (about 160 million years ago) when Africa became separated and began to drift slowly northwards. The next large block to break away was India, in the early Cretaceous (about 125 million years ago). New Zealand followed about 80 million years ago, only about 15 million years before the Cretaceous-Tertiary extinction event wiped out about 50% of all species on the planet, most famously, the dinosaurs.
As the age of mammals got underway, the continent of Australia-New Guinea began to gradually separate and move north (55 million years ago), rotating about its axis to begin with, and thus retaining some connection with the remainder of Gondwana for a considerable time.
About 45 million years ago, the Indian subcontinent collided with Asia, forcing the crust to buckle and forming the Himalayas. At about the same time, the southern-most portion of Australia (modern Tasmania) finally separated from what is now Antarctica, allowing ocean currents to flow between the two continents for the first time, which in turn produced cooler and dryer climates.
Far more significant as world climatic event, however, was the separation of South America sometime during the Oligocene, perhaps 30 million years ago. With the opening of Drake Passage, there was now no barrier to force the cold waters of the Southern Ocean north, to be exchanged with warmer tropical water. Instead, a cold circumpolar current developed and Antarctica became what it is today: a frigid continent which locks up much of the world's fresh water as ice. Sea temperatures dropped by almost 10 degrees, and the global climate became much colder.
About 15 million years ago, New Guinea began to collide with southern Asia, once again pushing up high mountains, and more recently still, South America became joined to North America.