Hi! I'll try my best to answer your question (: So Beadle and Tatum carried out an experiment that attempted to mutate the genes of the mould 'Neurospora crassa' and they also established metabolic chains that they believed must be occurring in the normal mould for it to be able to survive.
B + T hypothesized first that one gene controls the production of one enzyme and to prove this, they conducted an experiment using said mould. So first, they grew this mould in minimal medium (which is the minimum amount of nutrient requirements for it to grow) and the mould was then subjected to radiation to cause them to mutate. After this magic was conducted, the mutated spores were then transferred to that same minimal media to see if they would grow.
If the mutated mould was able to grow, it was discarded because this means that it was working perfectly fine. Referring back to those metabolic chains that B + T produced, they saw that for the mould to function perfectly, it needed to produce specific amino acids and enzymes and all of these needed to work together to grow it! I'll stick the chain down below for you vv
Precursor nutrient --> Ornithine --> Citrulline --> Arginine
where the nutrients are what's in the minimal media, and the rest are produced amino acids
So continuing on, obviously if the mutated mould could grow in this minimal medium, it must mean that the pathways are all working!! B + T discarded any mould that was like this, and only kept the mutated mould that COULDN'T grow in the minimal medium. Because this meant that one of the pathways must've been disrupted --> A disruption restricts the production of the required amino acid.
After this, B + T split this mutated mould into different sections and placed them in vials or test tubes supplemented with one of the required amino acids: Ornithine, Citrulline, or Arginine. If the mutated mould was able to grow in the vial, then its pathway must have been disrupted - the pathway required to produce that particular amino acid that was already in the test tube.
From all this, B + T were able to conclude that one gene must control the production of an enzyme to produce an amino acid. The exposure to radiation caused genes to be mutated, resulting in different enzymes being produced, therefore changing the amino acids making up the enzyme as well.
Over time though, the hypothesis was changed.
The one gene - one enzyme hypothesis turned into the one gene - one protein hypothesis because scientists discovered that not ALL proteins are enzymes. There exists other proteins that don't turn into enzymes, like structural proteins that are keratin.
Again, the one gene - one protein hypothesis was then changed to the one gene - one polypeptide hypothesis because scientists then discovered that one gene is not necessarily responsible for the structure of an ENTIRE protein, but only for each polypeptide chain making up that protein.
Hopefully this explanation wasn't too long, and I hope it helps (: