Biological evolution is a biological change over time. So the fact that people differ genotypically and phenotypically from their parents is enough to conclude that humans evolve biologically.
As for the specific means of biological evolution that led to the speciation of the "Homo sapien", there is a combination of genotypical and phenotypical analysis that is used to conclude that Homo sapiens biologically evolved from older species of apes; which evolved from some form of simpler eukaryotic ancestor. Unlike the case with people's immediate relatives, these ancestors to Homo sapiens no longer appear to be alive; therefore, since there is no primary source documenting their existence, fossils are likely the best means for deriving the aforementioned genotypical and phenotypical analysis. Unfortunately, the formation of these "body fossils" requires a very specific set of circumstances; either the organism must be immersed in sediment after dying, or it must be frozen, dried, or left in a deoxidized environment. For this reason, the discovery of fossils is a rare occurrence, and even rarer is the discovery of an in tact fossil. Furthermore, the mineralization that fossilizes these organisms destroys DNA that would be used for genotypical analysis; making older fossils less likely to have extractable DNA.
So, this leaves us with phenotypical analysis of the extremely-limited portion of fossilized organisms available to us. There are two main points of this phenotypical analysis that are useful with respect to the substantiation of biological evolution. The first, is the discerning of physical differences between fossilized organisms. This point is fairly simple to support, since physical differences between these organisms are readily-observable. An example of this is the smaller cranium, disproportionately longer limbs, and shorter stature of Homo habilis when compared to other humans--such as Homo sapiens. The second is the relative dating of these fossilized organisms. This can be done fairly accurately through radiometric dating; however, the depth of a fossil can also be used to estimate the its age, since older fossils tend to be deeper down than newer ones (because newer sediment settles on top of older sediment). An example of this is the fact that no fossils of humans (organisms within the "Homo" genus) have been found below the K-T line, while fossils of other organisms have been found below it.
The correlation between these two points is where evolutionary theory is formed. A good example of this correlation is the fact that fossils of organisms with simpler hearts (determined by separation of chambers, number of pumps, etc) tend to be older than fossils of organisms with more complex hearts. This shows a biological change in organisms' hearts over time; which in itself is biological evolution. Through comparisons like the examples I've listed, it has been observed that as time progresses, more complex/specialized/diverse organisms tend to arise. By using the facts that more complex/specialized/diverse organisms tend to appear over time, and that organisms are able to undergo biological evolution; it is concluded--backed by the physical fossil evidence mentioned in the above paragraph--that these newer, more complex/specialized/diverse organisms are to have biologically-evolved from older, simpler organisms.