There are many different viewpoints with widely different ideas about how this world came to be. I'll try to organize them in order from the most conservative to the most liberal (biblically speaking).
Young Earth Creationist
This is the position that God created the earth in six days about six thousand years ago.
The young earth creationist (YEC) believes this because it is the conclusion you come to with a plain reading of the Bible. The first 11 chapters of Genesis are considered to be a true and accurate history of the world and not just an allegorical story. Biblical inerrancy is the hallmark of the Young Earth Creationist. This viewpoint, however, does not mean that the YEC is disinclined to ignore science, on the contrary, God gave us science and knowledge and told us to "subdue the earth". The Bible is the authority and any apparent discrepancies between the Bible and what we see in nature can be explained by properly interpreting the facts.
Old Earth re-Creationist (Gap theory)
This is the idea that God created an original perfect world according to Genesis 1:1 and then something went wrong, probably rebellion of Satan and angels in heaven and then there was a Divine Judgment on the earth which caused the world to become formless and void in Genesis 1:2.
This idea hinges on whether the verse should read "The earth was formless and void" or "The earth became formless and void". There is some additional obscure support for this in Isaiah 45:18.
The Gap Theory is also known as the Ruin/Recreation theory. Supposedly God had to recreate everything about six thousand years ago after some indefinite period of time which occurred between Genesis 1:1 and 1:2. It is this period of time which explains the motivation for believing this theory. About 130 years ago, it had recently become common knowledge, at least within the scientific circles, that the geology of the earth proved that it must be billions of years old. What was a theologian to do with this? Where would he fit this billions of years into a Biblical model of creation and time? The answer was "in the gap between Gen 1:1 and 1:2". This became a very popular explanation as a result over the next century. In the last thirty years, it has fallen out of favor when consideration is given to how catastrophic events such as Noah's flood could explain the geological strata in the earth.
The progressive creationist pretty much accepts all standard models of how the universe and earth came to be including the Big Bang, stellar evolution, and planet formation over billions of years. The one thing they are against however is evolution. Instead, they believe that God performed special creative insertions of life into the world at various stages which explains all the species. These episodes of creative activity explain the word progressive.
The first chapter of Genesis is simply an long age framework divided into six "days", each one lasting millions or billions of years. Life shows up billions of years ago.
To hold this position, You have to be somewhat liberal in your interpretation of Gen 1-11 and on some theological issues. Hugh Ross, a brilliant man and charismatic speaker, is the main proponent of this view, and believes in pre-Adamic hominids (ape-men) with no souls, death before sin, no world-wide flood. These ideas have huge theological impact and so why does he believe these things? Because he believes Adam showed up about six thousand years and all of the geology and fossils were already in the ground. So you must have life and death before Adam. And you can't explain the layers of rock we see over the whole world by appealing to a world-wide catastrophic flood because Noah came after Adam and after the rocks were already laid down in layers by other naturalistic processes that he wants to preserve in his belief system.
Intelligent Design Movement
These are honest scientists who have no religious or biblical agenda but are simply bothered by the inability of Darwin's natural selection to explain the origin of complex systems of biological life. The specific complexity and appearance of design we see in life is better explained by appealing to an intelligent designer.
The proponents of the ID movement are agnostic about any particular designer and are not interested in appealing to the God of the Bible or to the Bible as any kind of authoritative book. Most of what they do is to critic the model of evolution by pointing out its weaknesses.
Because they are accredited, real working scientists, they are able to gain a lot more traction within the scientific community than a Creationist would be able to. Still, the ID movement is vigorously opposed by most mainstream scientists.
This group is typically quite liberal regarding the authority of the Bible and wants no part of being labeled a "foolish" creationist. Basically, they have no problem saying that God used evolution as his means to create life. Certainly an all-powerful, sovereign God could create life anyway he so chooses. The only problem is how to reconcile the meaning of the first eleven chapters of Genesis.
More importantly, Darwinism (random chance mutation acting through natural selection) is an unguided, purposeless material process with no room or need for God.
It used to be that an atheist was an eccentric. They had no plausible story for how we came to be. So they needed a plausible creation story and Darwin provided one. For the Atheist, naturalism must explain everything. In fact, science has now been defined to exclude any appeal to the supernatural.
Now, to be an atheist is mainstream. And Post-modernism is adding to its ranks daily.