Darwin was quite some time ago, and while he had some remarkable deductions for his day, and deserves credit for establishing the field, he's practically speaking irrelevant to the science of evolutionary biology. Even in Darwin's day, however, before genetics, his theory made a remarkable prediction: that taxonomy would be cladistic (to use the modern term). That is, you could organize species in a hierarchy based on common features.
You can't do this with e.g vehicles: there are features common to all pick-up trucks, features common to all Fords, features common to all passenger vehicles made after a certain year, and so on: it's immediately obvious that you can't make any sort of hierarchy based on features with any predictive value. A pickup truck bed doesn't tell you who made the alternator, the Ford logo doesn't tell you whether a vehicle has airbags, and so on. Remarkably, you can do this with plant and animal species, and the millions of cataloged species all fit this model: extreme confirmation of the prediction made from the hypothesis of common ancestry.
But that's all old-school, pre-genetics naturalism: 19th century and early 20th century stuff.
"Evolution" means "the statistical distribution of alleles in a population changes over time". Evolutionary biology is about statistical models of dynamic systems: good, solid mathematical models used in research daily. There's even an engineering aspect, as it's sometimes preferred for research organisms to manipulate the genome without directly splicing genes, or to ensure a stable population with a given modification for long-term research.
TLDR: read the Talk.Origins FAQ I've linked to the best starting point, but there's a wealth of information there, that directly speaks to the claims of skeptics of evolution. The materials are 20 years old now, but they're very well written arguments with counter-arguments with all the flame wars removed.