First of all, recorded human history goes back about 6,000 years. The earliest written documentation is believed to be from the Mesopotamian region of this era. I would submit that any prehistoric (before written documentation) timescale should be regarded with some trepidation as no one was there to witness it. In other words, anything that you are told happened more than 6000 years ago should not be swallowed whole, but chewed on for a while. This is not to say that the earth is only 6,000 years old. This is to say that there is no sure way of knowing beyond that.
Biological dating is an interesting science. It involves identifying natural biological processes with known rates, and then reversing mathematical interpolations of those rates to give estimates of dates back into history or prehistory. It sounds complicated, which is why I have been on the fence about it for so long. These systems absolutely make sense. Here is one example of these systems at work:
Tree ring dating:
This method a child could learn and understand. It is a method of dating involving tree stumps, or cores from unfelled trees.
The process:
Every year, no matter the climate, has a wet (cold) and dry (hot) season. In some places these seasons are much harder to distinguish from each other, but in others the difference is abundant. Every season leaves an impression on a tree. Trees grow well in wet seasons when their roots are getting plenty of water, and in the dry seasons they do not grow so well. The nutrients in the ground between a wet season and a dry season also differ, and, in a sense, both seasons leave a ring on a tree.

http://waynesword.palomar.edu/treedate.htm
As you can see in the photograph above (Douglas Fir), the small brown dot is the sapling tree. That represents its first year. The light, thickish ring surrounding it is a wet season where the tree grew well in a short amount of time. The small dark ring is a dry season where the trees growth was stifled. It is virtually a scar. A wet season and a dry season together make up 1 calendar year. You might also notice that some of the rings are further apart than others and some of the scars, or dry season rings, are larger or smaller than others. These represent particulars of those seasons. The large tan rings represent ideal growing conditions, which are lots of rain and lots of sunlight. Perfect, Central California type weather. The larger scars represent longer or more severe dry seasons, and can even represent forest fires. So if you count the rings on the tree sample above, you will find that this tree (at least what is shown in the picture) is about 32 years old.
Deductions:
Now considering that each tree ring is variable, depending on the season, we can reasonably assume that that same season in the same region would have similar effects on a similar tree, right? So, let's say that we cut down the above tree in June of 2003. If we found an old stump of another Douglas fir, and can see the rings on it, we can logically compare the rings of our tree to the rings of the stump. If we see a stretch of rings that match up almost precisely, we can logically assume that those represent the very same seasons as the one on our tree. So the years 1983 - 1988 on our tree match up perfectly with the outer 6 rings of the stump. What does this tell us? That the tree was cut down in 1988. This tree happens to have 85 rings, not just thirty. So now we can subtract 85 from 1988 and deduce that the tree began to grow in 1903. Now that that stump has a known date of origin, we can find another tree and try to match our stump up with that. We can match up, say the years 1910 - 1915 from our known stump to the other fir tree from the same region. The matching seasons on the other tree are not quite to the edge of the tree so we count back to the core from 1910 to see how old the tree is. This particular tree has 110 rings and 1910 falls at ring 95. So we subtract 95 from 1910 and deduce that this tree began to grow in the year 1815. We can also deduce, if it is a stump, that it was cut down in the year 1925. And on and on it goes. Now of course it can get more complicated than that, but in simple terms, this is the process of tree-ring dating. It's as logical as logical can get. Experts who use this method of dating have a tree ring historical record that goes back 8,000 years, meaning approximately 6,000 B.C., and 2,000 years further back than the written historical record.
Chemical dating involves identifying natural chemical processes with known rates, and then reversing mathematical interpolations of those rates to give estimates of dates back into history or prehistory. One example of that follows.
Radio Carbon Dating (Carbon-14 Dating):
This method is more complicated only in terms of the mathematical and chemical knowledge needed to understand it.
The Process:
(source: http://id-archserve.ucsb.edu/anth3/courseware/Chronology/08_Radiocarbon_Dating.html)
The earth's upper atmosphere is constantly bombarded by cosmic radiation (radiation from space). As this radiation enters the upper atmosphere, it causes nitrogen to break down into an unstable (decaying) form of carbon, known as carbon-14. This c-14 pollutes the atmosphere and as it is thrown to earth through storms and other phenomenon it attaches to living molecules in plants through photosynthesis. When animals eat those plants, they ingest the radioactive c-14 molecules as well. C-14 has been shown in laboratory to have a certain rate of decay. Since it is an unstable molecule it is constantly decaying into a stable one. This rate has been studied and the time it takes for a small amount of decay to take place has been multiplied out to the magic number of 5,730. Meaning that from what scientists discovered in the laboratory they decided that every 5,730 years, 1/2 of the c-14 molecule decays. This is what is called a half-life. Over the next 5,730 years, 1/2 of the 1/2 that remains will decay, leaving 1/4 of what was originally there, and over the next 5,730 years, 1/8 of the original molecule will remain, etc. This natural process also seems quite stable.
Deductions:
We can assume that herbivore animals eat plants their whole lives. Carnivores eat the herbivores in the same way the herbivores eat the plants, so c-14 can be found in any animal. When an animal dies, the replenishing of c-14 stops. This is the starting point of its logical decay. We can therefore determine the date of the animal's death by determining how much of the c-14 molecule is left to decay in the animal. Scientists know how long it takes for c-14 to break down, so if they find that a molecule is say 75% decayed, what does that tell us? Well, 75% is 1/2 of 1/2, meaning 2 half-lifes. We can then multiply the magic number 5,730 x 2 and find out how long ago the animal died, in this case 11,460 years ago. If it is 95% decayed, we can determine that as well, 100/2 is 50/2 is 25/2 is 12.5/2 is 6.25/2 is 3.125% so 5 half-lifes is a little too long. Actually 6.25/1.25 = 5%, the amount of c-14 leftover. So here we have 4.625 half-lifes for 95% decay, and 5% c-14 leftover. Multiply 4.625 by our magic number of 5,730 and we get 26,501.25. That is this particular animal with 95% c-14 decay died approximately 26,500 years ago, or the year 24,492 B.C. It should also be noted that most scientists agree that radio-carbon dating has about a 50,000 year limit on it's accuracy. After about the ninth half-life there is so little material left in the specimen (less than 0.2%) that it is very hard to accurately determine amounts.
Those are two of scores of dating methods that scientists use to date prehistoric material. And I haven't even gotten to geological methods yet. Wow. To be continued again.