1. What evolution is
2. Why it is accepted in the scientific community
3. Common misconceptions
4. Explain to the 'everyday person' the scientific terms used in evolution and what they really mean.
I also encourage a self-proclaimed creationist to make a post similar to mine, to help those who don't fully understand it.
The Theory of Evolution by Natural Selection
The two scientist most known to be associated with evolution are Charles Darwin and Alfred Russel Wallace. Both scientists formulated their theories independently, and each explained how organisms have adapted to different environments.
Darwin published his theory in 1859 in a book called On the Origin of Species by Means of Natural Selection. During this time, the leading theory was called "Special Creation", which stated that all the species on the earth were created independently by God. The key aspect to this theory held that species did not change.
Evolution Direct Definition
Change in characteristics over time
More precisely, the change in allele frequencies over time.
Micro Evolution
Micro Evolution is, in the most general sense, evolution that occurs within a population (Individuals can interbreed and are part of the same gene pool). Biologists who study this level of research indicate evolution is the change of gene frequency within the population.

This image shows a change in gene frequencies. This indicates that the population has evolved.
Processes of Micro Evolution
Mutation

Two green beetles reproduce. 1 of the offspring has mutated and has a brown gene instead of a green one.
Gene Flow

Gene Flow occurs when organisms from another population 'immigrate' to another population. This results in an increase in a certain gene.
Genetic Drift

Certain genes occur more frequently in a population randomly when members reproduce. In this case, brown increases while green decreases.
Natural Selection

This is the most exciting process in terms of observing how evolution works. As you can see in the image, the bird eats the green beetles more frequently because they are more easily seen. Therefore the brown beetles go on to reproduce and their frequency of genes increases.
Macro Evolution
This is the most controversial of the two (micro and macro) evolutionary process, not in the scientific community, but due to certain religious pressures.
Macro evolution is evolution occurring above the species level. Macro Evolution is not able to be observed first hand, unlike Micro Evolution, but that doesn't make it untrue. There are many scientific procedures that are followed to come to the proper conclusion.
The same exact processes involved in Micro Evolution occur in Macro Evolution, just on a much larger scale.

Biologists DO NOT question the holistic conclusions of Evolution, but they do question certain aspects of it. This is a short list of questions they are trying to answer...
1. Does evolution tend to proceed slowly and steadily or in quick jumps?
2. Why are some clades (A group of organisms that includes all the descendents of a common ancestor) very diverse and some unusually sparse?
3. How does evolution produce new and complex features?
4. Are there trends in evolution, and if so, what processes generate them?
Species Change as Time Passes
Darwin proposed that species that exist today have descended from preexisting species that changed through time.
Evidence
Transitional Forms
Darwin and modern scientists believe that extinct species in the fossil record are related to modern living species. Transitional forms are fossils of species with traits that are intermediate between those of older and younger species.
Example- Whales evolved from fox/small dog-sized animals. The oldest fossils suggest their oldest ancestor was a semi aquatic animal similar to hippopotamuses, due to their location in rocks that form in ocean deposits. Limbs reduced in size and became more aquatic.
This is an image of Australopithecus Afarensis which is accepted as an important transition form in the scientific community.
Extinction
Darwin and other scientists interpret the finding of extinct animal fossils as evidence that species are not static, but dynamic. They change and evolve into different species. If species have gone extinct, then they have changed through time. There have been more species that have gone extinct than there are species that exist today. Data suggests that species have gone extinct progressively throughout the history of Earth. One or two catastrophic events do not account for the amount of extinct species.
Structural Homologies

Structural Homologies are morphological traits that are similar. These can be similarities found in different aspects of an organism, including but not limited to such things as limbs (as seen in the above photo). All mammals descended from a common ancestor, and it can be observed that this common ancestor had the same foundation as its descendants.
Artificial Selection
Artificial selection can be described as an 'experimental natural selection'. Artificial selection can be done on both plants and animals. It helps us understand natural selection better due to environmental forces. Selective breeding and artificial selection is most evident in Broccoli/Cabbage/Cauliflower, which is descended from Yellow Mustard.

Evidence for Evolution: Summed Up
-Vast number of species have gone extinct
-Fossils of older species are similar to those of living species in the same area
-Vestigial Traits
-Populations of species are observed to be changing
How to Tell a Population is Evolving due to Natural Selection
1.Variation in the population. Mutations cause the changes seen in the organism. Genetic changes in DNA lead to structural changes which are past to offspring.
2.Heritable Variation. Variation in the genotypes (Genetic code for what can be observed) occur before an organism produces offspring, which causes it to be passed down.
3.Variation in Fitness. Fitness is the ability for an offspring to produce fertile offspring. Organisms in a population have a higher fitness than others and thus have offspring better adapted to its environment.
4.Selection. Those individuals with a gene that leads to better adaptation should have a higher reproductive success, and if it does, selection occurs and adaptation is met.
Common Myths in Evolution: What you need to know!
1. Evolution can only occur in populations. That is, individuals can not change during natural selection. Example: During a drought the beak size of individual finches does not become deeper, the average beak depth of the population increases over time due to higher fitness (remember, fitness means higher rate of reproduction) in deeper beaked individuals.
2. Evolution Doesn't Make Organisms "Better" Organisms that experience evolution do not necessarily get more 'complex' or 'better' due to evolution. They merely change to better fit their environment. For example, Tapeworms evolved from having a sophisticated digestive system to losing their digestive tract. No organism is higher than another.
3. Not all Traits are Adaptive. One of the most prime examples of this are goose bumps and the appendix. Both structures do not contribute or add to an organism's fitness and therefore are not adaptive.
4. Humans and Apes Share a Common Ancestor Humans did not evolve from Apes. They merely share the same common ancestor.
5. Natural Selection is Not Random Natural Selection is not a random process. The phenomenon of genetic variation due to mutation is random but those variants that cause a better 'fit' to the environment will become more widespread.
List of Terms Important in Evolution
Fossil- any trace of an organism that lived in the past.
Fossil Record- All fossils that have been found and described in scientific literature
Geologic Time Scale- Periods of geologic time in eons, epochs, and periods.
Transitional Form- Fossil species with traits that are intermediate between those of older and younger species
Vestigial Traits- Reduced structures that have no function or reduced function but are similar to functioning organs/structures of other organisms
Phylogeny- Family tree of populations or species
Structural Homologies- Morphological traits that are similar
Adaptation- heritable trait that increases fitness of an individual in a particular environment relative to individuals lacking the trait.
Fitness- Ability of an individual to produce offspring.
Evolution Is Just a Theory Argument
A theory is a proposed explanation for a very general class of phenomena or observation. Theories must have a proposed pattern and mechanism. Evolution has both of these. Inferring historical events from contemporary evidence is a valid research program in science. Remember that for some 150 years after the atomic theory was proposed, no one had actually seen an atom. Yet the theory was widely accepted as correct during this time. The theory of Evolution is supported by mountains of evidence and is generally accepted by every biologist. Of course evolution in a theoretical sense changes in minute ways, but the definition concerning how it works holistically has and will remain the same.
This is still a work in progress and will continue to add new parts to this thread. If you have any recommendations as to what should be explained or if you have any questions please post them and I will add them. This is a very brief start to a very large compilation that is planned to help educate the community.
