First, the Geologic Time Scale:
We can think of the large scale interactions between evolving life and the physical environment as a series of different Games of Life. Each particular Game represents some extremely broad set of interactions (rules). Introduction of a new Game into the "game room" (i.e., the totality of Earth's ecosphere) requires some major change: perhaps a new adaptation for interacting in a novel way, or the development of an entirely new way of life. In each game there are different roles: i.e., different ecological niches such as "top predator" or "largest forest tree" or "reef framework builder." The organisms in the different roles interact with each other according to the rules of the game. But the players in each role change through time: sometimes one species may inherit its role from its direct ancestor, but sometimes the new player might come from an ancestor in a very different role. Mass extinctions represent times when many roles might be "up for grabs"; many niches are vacated, and entirely different players might take up that role. (Similarly, when new games start, it is an opportunity for players from very different ancestors to take their spot.)
A Star Is Born: However, the VAST majority of the Solar System's mass is in the Sun. Gravitational forces of this mass starts fusing hydrogen into helium, and the Sun ignites. Originally it was dimmer than today, but still it shone. Solar wind and photon pressure began to sweep the Solar System clear of much debris.
Hadean Eon: 4.56-4.03 Ga
The Iron Catastrophe: Although the Earth is not a star, it (or at least the Proto-Earth) too went through a profound change in its earliest history. Originally the ices, organics, silicates, and metals would have been randomly mixed together, but a combination of gravitational heating, heating from impacts of planetessimals, and radioactive heating from some of the isotopes found in the silicates and metals caused the material of Proto-Earth to melt. The heaviest materials (mostly metals, especially iron and nickel) sank to the interior to form the core; the silicates "floated" on top to form the mantle. Ices melted into gasses and liquids, and they and organics got mixed in with other material. With a metallic core, Earth now had a magnetosphere.
The Primordial Atmosphere: Proto-Earth's original atmosphere would have mostly been hydrogen and helium, like the gas giants. However, it lost much of this atmosphere to a number of factors:
Bad Moon Rising: About 4.533 Ga, a Mars-sized planet (called "Theia" by some) collided into the Proto-Earth. Theia and a substantial fraction of the Earth's mantle was vaporized. The matter that remained in orbit around the Earth coallesced to form the Moon; the rest rained back down to the surface of the Earth. (So the matter of Proto-Earth + Theia became redistributed to form today's Earth + Moon).
As a result of the birth of the moon:
Archean Eon: 4.03-2.50 Ga
The first Game: Prokaryote-only communities: (Note: Archean (-EAN) refers to a part of Earth history; archaean (-AEAN) refers to a type of prokaryotic organism, and is thus a branch of the Tree of Life.)
Abiogenesis: origin of life:
Archean life would have very short food chains, but contained a great diversity of chemical pathways. Life would have been limited to the water. Most of the shallow seafloors, shores, etc. would be covered in algal/bacterial slime. As cyanobacteria spread, the oceans and atmosphere began to fill with oxygen.
Proterozoic Eon: 2.50-0.542 Ga
The Great Oxidation Event: Cyanobacteria (and eventually eukaryotic algae) release more and more oxygen into atmosphere. Between 2.7 and 2.4 Ga, most of this oxygen got absorbed by the copious levels of dissolved iron in the ocean water. This produced "rust", which accumulated on the sea floors in what is called Banded Iron Formations (or BIFs).
When the dissolved iron was all used up, BIF production stopped and the oxygen began to add to the atmosphere (and as dissolved oxygen in the water). Atmospheric levels of oxygen rises to about 10% of modern levels. The Great Oxidation Event produced the modern oxygen-nitrogen atmosphere:
The Great Oxidation Event would have devastated anaerobic organisms, which from that point onward would survive only in "extreme" environments.
New More Complex Games: origin of eukaryotes by endosymbiosis:
Eukaryotes remain unicellular for most of the Proterozoic. Life remains entirely aquatic, but food chains get more complex with diversifying levels of heterotroph consumers and detritivores and phototroph producers.
Snowball Earth: Methane is a greenhouse gas; as it was oxidized chemically it was reduced as a component of the atmosphere, and Earth cooled. Additionally, as the continents assembed during the Proterozoic and major orogenies occurred, carbon dioxide (another major greenhouse gas) got scrubbed out of the atmosphere by chemical weathering. Several different episodes of extreme glaciation happened: the so-called Snowball Earth events. The oldest was around 2.2 Ga; the others all in the Neoproterozoic. During these times, there was glacial ice as far as the equator.
The Garden of Ediacara: Origin of multicellularity: oldest evidence for multicellular organisms (rather than simple colonies) only about 600 Ma. By this point oxygen levels in the sea are much higher than before (although atmospheric oxygen only 10% of modern levels). Oldest animals (600 Ma) are very simple: suspension feeders and simple grazers. The vast majority of forms are only soft tissue: teeny tiny shells are the only hard skeletons, and only at the very end. Much of the sea floor still covered by simple algal mats. Land remains barren.
Paleozoic Era, Cambrian and Ordovician Periods (542-488 Ma):
The Cambrian Explosion: In a relatively short period of time, many different sorts of animals evolved the ability to form shells of calcium carbonate, calcium phosphate, or silica. First only very small, within a few million years they formed shells big enough to see with the naked eye: the so-called "Cambrian Explosion".
Ecosystems became much more completx: the first burrowing animals and better grazers resulted in the loss of algal mats disappear except for extreme environments. Many diverse forms of life, but lower diversity than later seas. Many new interactions between animals and algae. First reefs (sponges).
As early Paleozoic continues development of more diversity and more complex marine ecosystems. By end of Ordovician Period, food webs nearly (but not quite) as complex as in modern seas.
Paleozoic Era, Silurian and Devonian Periods (488-359 Ma):
The New Seas: First really complex reef communities: as diverse as modern coral reefs, but different players. Food webs arguably as complex as in modern oceans, but many more types of attached motionless animals than in present seas.
Conquest of Land: Colonization of land and freshwater by green plants, various arthropods, fungi, vertebrates, and some others. Development of first soils. Plants begin to bind the soil together. Atmospheric oxygen levels increase, as there is an even larger source of photosynthesis than before.
Paleozoic Era, Carboniferous and Permian Periods (359-251 Ma):
The Forest Primeval: First forests and complex terrestrial and freshwater communities. Buried remains of these coal swamps form much of today's coal deposits.
Colonization of drier continental interiors. Development of seeds, wings, and shelled eggs allow plants, insects, and vertebrates (respectively) to better colonize the interiors of the continents away from lakes, streams, and swamps. Diverse terrestrial communities form.
Permo-Triassic Extinction: Tremendous global changes associated with one of the largest episodes of volcanism in Earth's history produces huge mass extinction event 542 Ma. Major players in both terrestrial and marine realms wiped out. Number of species after extinction event only about 10% what was found before hand.
Mesozoic Era (251-65.5 Ma)
The Age of Reptiles: Diversity builds back on land and sea. Rise of many groups of modern forms, including: modern insects; modern-style crustaceans and mollusks; advanced bony fish; modern-style amphibians; early mammals (which become very diverse at small body sizes); birds and other feathered dinosaurs; flowering plants (by mid-Mesozoic). Nearly all major terrestrial roles are in place by the 200 Ma, but the players are different than those of today: dominant large terrestrial and marine animals are all reptiles.
In the marine realm, mid-Mesozoic shift from communities dominated by motionless attached animals to ones of modern style, dominated by moving mollusks, crustaceans, fish, etc.
Death From Above: At 65.5 Ma, an asteroid approximately 10-15 km diameter struck the Earth in what is now the Yucatan Peninsula of Mexico. The devestation brought by this blast (including major pulse of heat from re-entering debris, impact "winter" causing freezing temperatures and collapse of photosynthesis for weeks or months, and greenhouse "summer" afterwards by high levels of carbon dioxide released), on top of other environmental changes already happening, brought a mass extinction that ended the Age of Reptiles.
Cenozoic Era (65.5 Ma – now)
Age of Mammals: Surviving forms take over abandoned ecological niches: for example, most groups of large reptiles on land and sea are replaced by mammal groups. Diversity builds back up in land and sea.
Towards later Cenozoic Era, rise of grassland communities and meadowland communities. During last 2.59 Ma the Quaternary Ice Ages: advance and retreat of glaciers.
Origins of Humanity: Rise of plains-dwelling primates as part of expansion of grasslands in Africa about 7 Ma. Diversification leads to rise of anatomically modern Homo sapiens by ~190 ka, behaviorally modern humans by ~70-60 ka, which then spread to every habitable part of the glove. Agriculture by ~10 ka: humans regionally begin to dominate their ecosystems.
Or, for The Simpsons version of this:
(Or the story backwards, courtesy of Guinness):