All observations and discoveries confirm evolution.
Scientists adduce many evidences to support the theory of evolution. Some aspects are still the matter of controversies and disputes, some are not well understood, but the fact that evolution takes place in nature is widely and undoubtedly documented.
Like all other theories, the evolutionary theory should lead to testable statements, and ineed it is so.
 

Evidences of evolution are divided into two groups: indirect and direct.

Direct evidences are fossils
and other paleontological data and examples of evolution that take place now. Biochemistry, genetics, physiology, comparative anatomy, embryology, biogeography offer indirect evidences.

DIRECT EVIDENCE
fossil - recognizable fragment, or an impression left by an animal or plant preserved in the Earth crust

Formation of fossils
Usually when an organism dies, its body decompose. Fossils formed only if some matter (suspension of small mineral particles in water, sand, mud, bog, asphalt, volcanic ashes)  covered it and protected from carrion eaters, air, microbes and other. This is why land and soft-bodied organisms fossils are less frequent.

Types of fossils.
What are the kinds of animal fossils?

• In original structure, porest have been filled with minerals. For example: bone filled with calcium carbonate or silica.
• Natural moulds and casts that formed after decomposition of the original tissues. When the hole was filled by minerals before tissues were resolved or by sediment replicas of the internal structure were made.
• Imprints, like tracks and footprints. For example impression of feathers of Archaeopteryx or footprints of dinosaurs from Paluxy River.
• Also unaltered remains preserved in frozen soil, asphalt lakes, peat bogs. Mamooths bodies from Pleistocene Epoch discovered in frozen soil of Siberia were such well preserved, that is was possible to analyse its DNA.
• Organisms, mainly insects trapped in resin of ancient conifers hardened into what is called amber.
• Fossilzied excrements, called coprolites. They often contain hard parts of digested organisms, such as bones or fish scales.

What about plants?

• Carbon films that retain the shape of original organisms. Many fern fronds were fossilized this way.
• The original substance, such as wood, has been replaced by mineral matter. This is called petrifaction or petrification. This type of fossils were found in Arizona, where a forest was petrified.
• Imprints, of leaves for example.
• We can also learn about plants from pollen and spores that have been preserved in sedimentary rocks.

As you see, usually what we can find are fragments of hard parts of body or imprints. To reconstruct the appearance of the individual we have to combine fossils we have (sounds like a puzzle, doesn’t it?) and supplement it with soft parts (muscles, skin, hair, feathers). On the basis of bones, their shape and the points of muscle insertion palaeotologists can tell about the posture and the way of locomotion. From fossils we can also learn about when and were organisms lived and, if we have enough of them, about evolution.

Some fossils are useful for dating. If they existed during short period of time (geologically), were widespread and are easy to recognize (which means small for example) they can serve as index fossils, typical for paricular zones.

  Evolution takes place now!

People are changing the environment. Plants and animals react to these changes and we can observe evolution happening now.

In industralized areas, where lots of dust settle on ground and plants brighly coloured moths are replaced by dark ones. Bright moths are easy spotted by predators. Dark moths are less visible and have greater chance to survive (reproduce and transmit this feature to their young).

By using insecticides we cause origin of races of pests immune from what we use. Also amongt microbes we can observe rise of strains, that are resistant against medicines, such as antibiotics or sulphonamides.

These occurences are unintended results of human activity. But we also change our environment intentionaly. These are agricultures and animal husbandries. We select individuals in consideration of features we need. This is what Darwin called artificial selection. As a result there are now hundreds of breeds of dogs, cats, pigeons.