The most basic direct evidence of evolution is our direct observation of evolution occurring. This is also the most basic lie which creationists tell about evolution because they constantly claim that evolution has never been observed when, in fact, it's been observed both in the lab and the field repeatedly. Creationists count on this lie getting traction because they lie about what evolution is and repeat the lies often enough that they are believed through sheer, dishonest repetition.
Observed Natural Selection
What's more, the observed instances of evolution occur in the context of natural selection, which is the basic explanation for evolutionary changes in the theory of evolution. The environment can be seen to exert a "force" on a population such that certain individuals are more likely to survive and pass on their genes to future generations. There are numerous examples of this in the literature, none of which creationists read.
The fact that natural selection works is important since we can be sure that there have been environmental changes in the past. Given this fact, we would expect organisms to evolve to fit their environments. (Note: It is widely accepted that natural selection is not the only process at work in evolution. Neutral evolution also plays a role. There is some disagreement as to how much each process contributes to evolution over all; however, natural selection is the only proposed adaptive process.)
Ring Species & Evolution
There is a specific type of species that bears some discussion: ring species. Imagine a straight line across some significant sized geographical region. There are two distinct but closely related species at either end, say point A and point B. These species do not typically interbreed, but there is a continuum of organisms along the line that stretches between them. These organisms are such that the closer you are to point A the more like the species at point A the organisms on the line are, and the closer you are to point B the more like the species at point B the organisms are.
Now, imagine bending this line such that the two endpoints are in the same location and a "ring" is formed. This is the basic description of a ring species. You have two nonbreeding and distinct species living in the same area and strung out over some area a succession of creatures such that, at the "farthest" point on the ring, the creatures are largely hybrids of the two distinct species at the starting points. This is significant because it shows that intra-species differences can be large enough to produce an interspecies difference. Differences between species are therefore the same kind (though not in degree) as the differences between individuals and population within a species.
Nature only appears to be divided up into discrete types at any one time and place. If you look at the biosphere as whole throughout time, the "barriers" between species appears much more fluid. Ring species are an example of this reality. Given our understanding of the genetic mechanisms of life, it is reasonable to think that this fluidity extends beyond the species level to higher order taxonomic differences between species.
As with the basic genetic mechanisms, creationists will argue that there is a magic line across which evolution may not move. This is why creationists will define macroevolution differently than evolutionists. Since speciation has been observed, macroevolution has been observed according to the evolutionist; but to a creationist, macroevolution is a change in kind. Even creationists generally won't argue that natural selection doesn't take place. They just say that the changes that can take place are limited to changes within the organism's kind.
Again, based on our understanding of genetics it is reasonable to think that it is possible for large-scale changes to occur, and that there are no rational reasons or evidence to support the idea that they can't occur. Creationists act as if species have some hard-coded distinctiveness that separates them from one another.
The idea of species is not completely arbitrary: for example, in sexual animals lack of reproduction is a real "barrier." Unfortunately, the idea that living organisms are divided in some magical way which makes them distinct from one another just isn't supported by the evidence. Ring species demonstrate this on a small scale. Genetics suggests no reason it should not be true on a large scale.
To say that species can not change beyond some "kind" boundary is to create a totally arbitrary dividing line that has no biological or scientific basis — that's why creationists who try to make arguments about "kinds" can't provide a consistent, coherent, useful definition of what a "kind" is. The differences immediately "below" the boundary will be the same as the differences immediately "above" the boundary. There is no rational justification for drawing any such line.
The important thing to know is that evolution has actually been seen and documented and that the observed instances support the idea of natural selection. It is logical and reasonable to conclude that in the absence of something to prevent it, a succession of speciation events would eventually lead to a divergence where descendant organisms would be classified in different genera, families, orders, etc.