I know "À l'œuvre, on connaît l'ouvrier" is a proverb, but what does it mean?
It means that one knows the worker by looking at his work.
À followed by a noun, like in this sentence, can introduce a means. It's somehow similar to known locutions such as à vue d'œil or à pied. Other common examples:
On le reconnait à la couleur.
Cela se juge au poids.