How do we determine the age of fossils ?

<<I can't seem to find a basic straightforward answer>>

That has much to do with it not being straightforward. Two broad groups of methods can sometimes be used indepedently of each other, but other approaches are also sometimes applicable.

Relative dating

Most common is relative dating via stratigraphy. Rock layer B, which happens to contain fossils in this case, is above layer A but below layer C. As that's the order they were deposited in, B can be dated as younger than A and older than C. You've just also dated the fossils.

Adding more detail to that comes from geological surveying all over the place, knowing that certain species of fairly common fossils happen to be restricted to a relatively short space of time over a reasonably wide geographical area (for example, should an ammonite species only occur during five million years of the Middle Jurassic, then the rock it comes from is almost certainly of that age), a knowledge of the chronological range of all kinds of critters and plants... Actually, using every line of evidence that a locality may offer. Should the fauna and flora of your locality in general and in detail correspond closely with those from sites elsewhere, then your locality is also of a similar age.

Absolute dating

Sometimes, a rock layer may contain something that can be dated in accordance with radioactive decay. Ancient volcanic ash can be cooperative. The amount of decay of the mother isotope into its products can be measured, the rates of decay are known and they happen to be consistent. That can allow you to work out how many years ago that decay process began and, therefore, how long ago that ash was deposited. And that's going to be the age of the rock the ash is in.

Other stuff

There are other methods as well. For example, much is known about switches of Earth's magnetic polarity, and there have been close to 60 such events over the past 65 million years. Whether the magnetic in to the north or the south has an effect upon the crystallization of rock. Should the crystals be pointing south, then that rock didn't form when the magnetic pole was north.

Don't always expect straightforward answers.

Update

<<The most common way is what's called carbon dating.>>

Almost complete garbage. With a half-life of around only 5,700 years, carbon-dating is useless with remains older than (at most) 50,000 years. There won't be enough of the stuff left for reliable measurements. Furthermore, relative techniques are used far, far, far more commonly than radiometric methods as the majority of localities don't contain anything that can be radiometrically dated.

The most common way is what's called carbon dating. All elements on the periodic table have isotopes. Some of these isotopes have a very specific half-life (the amount of time it takes for an element to break down into half of the original amount). For example, a medication may have a half life of 24 hours. So 24 hours after you take the medication, half of it is still left in your body. Then after another 24 hours, a quarter. After another 24 hours, an eighth...and so on.

There is a specific carbon isotope that has a precise half life. By measuring the amount of carbon isotope still in the fossil, scientists can backtrack to see what the original amount of isotope was in the fossil, and then with a few calculations, the amount of half-lives the carbon isotope went through, and thus, the age of the fossil.

Don't know what your scientific or math background is so it may be hard to understand.

Carbon dating can only date things up to approximately 60,000 years old due to the half life of the unstable carbon isotope thus most fossils cannot be dated this way. Older fossils are dated using other forms of radiometric dating such as AFTA and ZFTA (apatite fission track and zircon fission track), argon - argon dating, uranium - thorium, potassium- argon etc...

Absolute dating of rocks or the inclusions in them allows the fossils contained in rocks of the same age to be dated. Occasionally the fossils themselves contain the radioactive isotopes required for dating.

Once the ages of fossils are known they can be used to relatively date rocks in which they are found, this is much cheaper and faster than attempting radiometric dating of every rock you come across!!!

A (radioisotope dating) and D (relative dating by potential of assessment to index fossils). there is likewise Carbon -14. this methodology of determinging fossil a while in basic terms works with those below 10 000 years previous. you could bypass to Wikipedia, the ffree encyclopedia.