People often misunderstand what science is about...
I'm afraid you've misunderstood what science is about, too.
The Scientific Method as you've described it is a wonderful thing. It's a driving engine behind our modern knowledge. But it's not the only engine
. There are whole realms of sciences - astronomy comes to mind - where direct controlled experimentation isn't possible. But they're still sciences. When we need to identify them, we call them "observational sciences".*
Basically these are sciences that let nature do the experiments for us. Astronomy has a whole night sky filled with billions and billions of stars. So even though we never set up an experiment, we still have a wealth of data sitting ready for us to analyse. In the same way, evolutionary biology never set up an experiment,** but there's so much evidence - fossils, morphology, genetics, geographic distribution - that we can connect the dots and build reliable theories.
And yes, those theories can be falsified, if we just find some evidence against them. We never have.
Wikipedia has an extremely long article, reflecting the extremely extensive degree of evidence [http://en.wikipedia.org/wiki/Evidence_of_common_descent]. To scientists, evolution is not even slightly controversial.
* (Actually, few sciences are purely one category or the other. We're not that stupid; we can and do combine evidence from experimental and observational sources. Oh, and there's a third group - formal sciences, which are based on reasoning. Computer science and mathematics are examples of formal sciences.)
** (Well, actually, experiments have been done. If you pick the right species, it's not hard.)