In 1953, Crick and Watson (with some help from Rosalind Franklin) determined the structure of DNA. But despite knowing what the molecule looked like (a double helix) and what it did (encode for proteins), nobody knew how, exactly, that translating and encoding happened.
There had to be, Crick had postulated, some sort "bilingual" molecule, an intermediary that could talk both to DNA and to the ribosome that created the proteins.
Ultimately he was right—that's exactly the job that transfer RNA does. But it took decades before anyone actually knew what tRNA looked like.
In 1956, Paul Zamecnik, a scientist working at Harvard, and his group of researchers made what one of them, Mahlon Hoagland, would later call "a fortuitous discovery." Hoagland says, in this interview:
Zamecnik himself and an associate of his discovered that the amino acids...not only were activated as I had discovered but were then subsequently transferred to an RNA molecule. This was a totally mysterious finding because there was no evidence that that RNA that it was attached to—had any role in protein synthesis at all.
What he's talking about here is how, in cells, the information from DNA gets transformed into the proteins, with amino acids as the building blocks and RNA doing the shuttling in between. This is how cells work—how life works. That little mysterious molecule doing the shuttling, it turned out, was transfer RNA.
Almost a decade later, another group of scientists sequenced its nucleotide bases. By the early 1970s, molecular biologists had a pretty good idea of how protein synthesis worked. You can see the basics in this really wonderful video, produced at Stanford in 1971 and narrated by future Nobel winner Paul Berg:
But although enough was known about transfer RNA (tRNA) that it could be represented by a bearded man dancing around shirtless, no one knew how it was actually structured—the best hypothesis was that it was shaped like a cloverleaf. Around the same time, a couple different labs had been working to crystallize tRNA so that they could get a good look at it. Finally, in 1973, someone succeeded. The New Scientist reported:
The molecular architecture that emerges bears little resemblance to any of the structures proposed on indirect evidence. It consists essentially of a letter L…The "anticodon"—which recognizes the codeword for the amino acid is at one extremity of the L-shaped molecule, with the amino acid receptor site at the other.
The cloverleaf hypothesis wasn't entirely wrong, but no one had predicted that it would be folded up into this L shape. This, as the New Scientist wrote, was the first time in about 20 years—since scientists had used x-ray crystallography to get a good look at the DNA's double helix—that they'd been able to use it to see the structure of another tiny molecule, essential for life as we know it to exist.