From Genesis, God created Adam and Eve. How come we have so many races on earth if we came from the same parent? Is it because people changed physically by adapting to various climates? Or races were made when different languages were introduced in Genesis 11 vs 6-8? How can I explain the human race diversity given the literal Biblical account?
Based on the wording of your question, I assume you want a literalist/young earth creationist perspective. This isn't the only perspective in Christianity. Plenty believe in evolution, or one form of Old Earth Creationism or another. The last portion of this answer, on particular, will likely be jumped on by the OEC and Evolutionist crowds, as it's specifically a literalist/young earth creationist view.
Technically, from many Creationists point of view (Kent Hovind, Ken Ham, Henry Morris, me) there is only one "race" . The "human" race. The idea of dividing up God's people into an artificial grouping based on superficial differences is wrong, anti-Biblical, and offensive in and of itself.
"Race" is strictly an evolutionary concept used by (some) to rationalize their white racism. But from the beginning it was not so! "God that made the world and all things therein; . . . hath made of one blood all nations of men for to dwell on all the face of the earth" (Acts 17:24,26). "Have we not all one father? hath not one God created us? why do we deal treacherously every man against his brother?" (Malachi 2:10).
The thinking described above is known as "scientific racism", and is generally denounced today, for good reason.
An interesting observation, taken from http://www.bible-truth.org/race.htm
The question we must first answer is: "Are there races of men?" The difficulty of classifying man into races has been shown. Perhaps a better term would be "varieties" of man. Even evolutionary science concludes that all existing varieties of man are members of the same species.2 Inter-racial marriages are common and children are produced with no biological difficulties. Prominent anthropologist, Ruth Benedict in her book, "Race: Science and Politics" stated the peoples of the earth are a single family and have a common origin.3
Once supposed biological differences, such as dissimilarity in blood, have proven to be incorrect. Blood is classified according to type, and all types are found within all supposed races of man. Blood transfusions are based on types A, B, AB, and O and are given without regard to race.4 It has also been supposed that different races have differing intelligence levels. The false and racist idea concludes that the Caucasian race is the most intelligent with the Negroid race being the least intelligent.
Modern testing of the races has shown that intelligence is not a measurement of race, because intelligence levels differ greatly with individuals within every race. Further cultural influence and advances account for most supposed examples of differing intelligence. 5
The concept of "race" isn't Biblical, either.
The next question is "Can race be Biblically defined?" The term race does not appear in the Bible. The Bible refers to differing peoples in terms such as family, tribe, people and nation. It groups people according to familial relationships and then into nationalities. An example of familial relationship is found in Genesis 10, where the genealogies listed are grouped by family. It should be noted that nowhere are the sons of Noah associated with race or color. An important passage on this matter is found in Genesis 10:5:
"By these were the isles of the Gentiles divided in their lands; every one after his tongue, after their families, in their nations" (Gen. 10:5).
The differences in skin color, hair color, curliness/straightness of the hair, and other traits that we, in our society call "different races" are minor variations. They can easily be attributed to simple genetic complexity -the same mechanism that causes my children to not look exactly like me, but similar to me, multiplied over many generations. As families became more spread out over the globe after the flood, the differences became more pronounced within the groups.
The historical answer to this question has been that Noah's three sons - Shem, Ham, and Japeth - represent the three major races - the Whites, the Blacks, and the Asians. Here, for example, is a reference showing this understanding. Hal Lindsay's Late Great Planet Earth also made reference to this common myth that Noah's son's were the progenitors of the races. The Table of Nations is Genesis 10 is considered a "map" of the various races, and is used to pin the various movements of Noah's children.
Japeth's tents being "enlarged," for example, explains the high populations amongst Asians.
Shem's blessing, since he was White, shows that from the beginning God loved Whites more than Blacks, and his plan was always for the White race to be blessed amongst the rest of the World. Being as Jesus, the ultimate White Anglo-Saxon Protestant European, descended from Shem, it just proves how much God loves White people.
And, of course, the fact that Ham was cursed (as was Caanan!) shows that Blacks too are supposed to be subjagted by everyone else, because, after all, Whites are only carrying out God's plan!
(If you haven't figured this out by now, I most definately do NOT believe any of this. I'm just trying to reflect what would have been considered a fairly normal 18th / 19th Century understanding of where the idea of race came from. I feel obliged to say "Thank You, God for changing our understanding!!)
People have many genetic attributes. Of course genes are passed on to your children.
It's a well-understood biological phenomenon that small populations can lose material from the gene pool. For example: Suppose we have a genetic trait that has possibilities, called "alleles", big-A and small-a. We have two people who each have both alleles, that is, they both have Aa. Each passes one of the two on to their children. Which the child gets is basically a toss-up. Say that just by the luck of the draw they both pass the big-A to all their children. Then the small-a is lost. If no one from outside joins the community, the small-a is lost forever. Or if they manage to pass both A and a to their children, but more A than a, than in the next generation there may have yet fewer a's, and in the next fewer still, until it dies out. This can happen just by chance, or if there is something in the environment that favors A. Like if a gene makes you allergic to oranges and oranges are the main source of vitamin C in this particular place, then that gene will tend to die out. This is called natural selection. (And by the way, while natural selection is often associated with evolution, it was actually first described in a scientific paper by a creationist, Edward Blyth.)
After the Flood, Noah and his family must have had the genetic material for all the races that exist today. Perhaps, for example, Japheth was white and Ham was black and Shem was yellow, or perhaps they had the genes for all the races more mixed together between them. Either way, after the Tower of Babel people started to spread out across the world in different directions. The population at that time was still small, and little subgroups that went out would have been smaller still.
So, for example, the people who went to Africa either happenned to all have the genes to be black and so all their descendants were black, or the people among them with white, yellow, and red genes all died out and only the blacks survived to pass on their genes. It's commonly argued that black skin is better for survival in hot jungle environments and white skin is better for colder environments, so the white gene survived in Europe and the black gene in Africa. I used to think that was established fact, but lately I've heard it argued that it's just an assumption based on the fact that people in Africa are mostly black, etc. I don't know enough about the biology of it to have an informed opinion. Either way, whether non-blacks died out because of environmental factors or pure chance or were never there to begin with, Africa ended up black and Europe white.
So as people spread out and sub-populations separated, some genetic diversity in the various communities was lost. Blacks separated from whites separated from asians.
Note that genetically, the difference between races is pretty minor. I read somewhere that race is controlled by just 4 genes. (Sorry, can't give a reference on that, can't swear that it's true.) In India it's not uncommon for families to have a broad range of skin colors, and it's becoming increasingly common in the US as marriage between people of different colors becomes more common. There's no need to theorize that the genes for different skin colors somehow came along later, whether by mutation or some miracle. It would not have been at all difficult for 8 people to have all 8 alleles. Two people could have all the genetic material for all races, as long as they don't have any common alleles between them. (i.e. Adam could have been coal black and Eve lily white or vice versa, or each could have been a middling brown, or some other combination.)
According to the YEC perspective, races were created (or at least furthered; see AffableGeek's excellent answer) at the Tower of Babel. In Genesis 11:6 it states "The Lord said, 'Behold, they are one people, and they all have the same language...'" Then in verse 7 and 8, it states "'Come, let Us go down and there confuse their language, so that they will not understand one another’s speech.' So the Lord scattered them abroad from there over the face of the whole earth; and they stopped building the city."
This scattering thus resulted in different races.