Darwin, Natural History Museum, London

In a darkened space filled with the sound of birdsong, two preserved bird skins lie on a velvet cushion. For a blockbuster exhibition transferred from the US, I had expected a bigger and brasher opening. Instead, this introductory display is striking in its modesty, with a clear message of the primacy of specimens and the evidence they afford.

Of course, these are no ordinary birds, but two of "Darwin's finches", collected by Charles Darwin when he visited the Galapagos Islands in 1835. The subtle differences between them - which he only noticed after he had left - reflect the differing habitats and lifestyles the birds adopted following their physical separation on different islands of the archipelago.

While these birds have become iconic objects in the history of biology, they are just a small part of the vast body of evidence Darwin gathered to support and refine his theory of evolution by natural selection, not only from his time on the Galapagos, but over his whole life.

In crossing the Atlantic, this exhibition from New York's American Museum of Natural History has been give a new subtitle, Big Idea, Big Exhibition. Although its layout is roughly chronological, the journey it follows is Darwin's own internal one, from "wide-eyed observer" to "profound analytical thinker", as his Big Idea took shape.

There is no shortage of evidence to inform our understanding of his thinking: Darwin was a prolific writer of letters and notebooks, and the presence of primary documents, both originals and facsimiles, give this exhibition authority and depth.

Darwin's intellectual journey was kick-started by a physical voyage, his five-year circumnavigation of the globe as naturalist and captain's companion on HMS Beagle between 1831 and 1836. Throughout that time, he made copious notes of his observations on a vast range of biological, geological and anthropological phenomena.

As a young man, he considered himself to be first and foremost a geologist, and on his return to England he had at least two books about geology planned, as well as "some ideas he planned to keep to himself".

Of course, it is these ideas we are most concerned with here. While the geological observations merit a mention, it is Darwin's views on the animals and plants he found during the five weeks he spent on the Galapagos Islands that dominate the first part of the exhibition.

Models, specimens and indeed live animals give the exhibition breadth and diversity, reminding us that Darwin's observations were rooted in his love of looking at nature at work.

This approach continues throughout, with the personal and domestic intertwined with the intellectual and philosophical, as Darwin settled into a happy and comfortable life at Down House in Kent.

His relentless studying often took the form of a family adventure, tracking bumblebees, counting plants and visiting the zoo, while early drafts of On the Origin of Species were reused as children's drawing paper. Part of his study is reproduced here, where specimens and instruments are displayed alongside family artefacts.

The most touching is a writing case belonging to Darwin's daughter Annie, whose death at the age of 10 devastated Darwin and may have contributed to his belief in the Christian afterlife being challenged.

Much of the latter part of the exhibition is a comprehensive explanation of the Big Idea itself, with evidence drawn from across the living, and fossil, world. This exhibition offers few new insights into Darwin's work: other upcoming exhibitions, such as the Darwin the Geologist at the Sedgwick Museum in Cambridge, will help us to view him in a different light. But this is a fresh and intelligent telling of a well-known story.

The exhibition is attractively designed, with graphic panels to packing in plenty of text that is presented in manageable nuggets.

Heavyweight ideas are balanced with anecdotes and quotes. Apart from an incongruous computer interactive, this exhibition makes little concession to younger audiences, and is the better for it, yet there is plenty for secondary school science students.

In an ideal world, there would be more specimens and better lighting, but these are petty niggles -the lighting needs to be low to protect the objects. The unfortunate decision to display a Braille copy of On the Origin of Species behind glass sounds a single jarring note at the very end en route to the exhibition shop, where cuddly Darwins sit side by side with academic treatises.

It is the central part of this exhibition, in which a robust and effective defence of Darwin's theory is presented, where it really packs a punch. For more than 150 years the theory has caused controversy: today's debate about intelligent design is just a new take on old objections.

Here, detractors are addressed head on by a clear outline of the difference between what we might informally call a theory ("I have a theory that X fancies Y") and a scientific theory, which is a well-supported explanation for understanding and unifying many facts, laws and hypotheses.

This exhibition makes it clear why Darwin's theory of evolution by natural selection is the latter, and therefore has such fundamental importance to modern biology, a message reinforced by engaging quotes from active researchers.

What the exhibition doesn't do is waste time entering into arguments that are essentially religious, not scientific, in nature. As we approach the bicentenary of Darwin's birth and all the celebratory events that are planned around the country, museums with scientific collections need this sort of confidence and clarity to help the public understand what science is, and what it isn't.

I'm not just referring to evolution: from an MMR scare based on only 12 case studies, to the pseudoscientific claims made for face creams, we would all be empowered by a better understanding of how evidence should (and shouldn't) be used. Evidence is what fills our museum stores and cellars: let's make the most of it.

Liz Hide is the museum development officer at the University of Cambridge