The history of life on Earth is in its fossils, and more than 99% of all species that ever existed are now extinct.  (Note that this is a lousy record for any sort of intelligent designer.)  We have extensive fossils showing how species have come and gone over the last several hundred million years.  Here are just a few examples:

• Trilobites appeared over 500 million years ago and existed for 300 million years (with over 15,000 known species).
• About 375 million years ago, land animals were evolving from fish.
• Dinosaurs (with an estimated 200,000 species) lived 251 to 65.5 million years ago.
• Horses are descended from the cat-sized Eohippus of 50 to 60 million years ago.
• Whales are descended from land animals of 52 million years ago.
• Humans are descended from a long line of hominids, over at least 4.4 million years.

The dating methods for determining the ages of fossils and rocks are well established.  They usually depend on the radioactive decay of different isotopes of elements, and can be used on objects that are hundreds to billions of years old.  For an in-depth explanation, see Accuracy of Fossils and Dating Methods.

The evidence for evolution of life is overwhelming and conclusive.  This evidence is not just in the fossils, but also in the body parts and genes of almost every living thing.  If you have any doubts, take a little time to learn the concepts of evolution, then spend a few hours in any natural history museum or public library.  If your mind is at all open, you will see the evidence.  Remember, ignorance of how evolution works is no argument against it.  The basic Theory of Evolution is completely solid, and will continue to be updated as we learn more about the complex history of life.