How do linguists reconstruct a language nobody wrote down?
By comparing descendant languages systematically and working backwards, using the fact that sound change is remarkably regular — the same sound in the same environment changes the same way throughout a language.
The comparative method, step by step:
Assemble cognates — words in related languages that appear to descend from a common ancestor, chosen from basic vocabulary less likely to be borrowed: body parts, kinship terms, numbers, natural features.
Find sound correspondences. Not resemblance, but recurring systematic matching. If Latin p corresponds to English f in word after word — pater/father, pisces/fish, pes/foot — that regularity is the evidence. A handful of similar-looking words proves nothing; a consistent correspondence across hundreds does.
Reconstruct the ancestral sound most plausibly producing all the descendants, given what is known about how sounds typically change. Reconstructed forms are marked with an asterisk.
Reconstruct grammar and vocabulary the same way.
Why it is trustworthy. Sound change being regular rather than word-by-word is the core insight, established in the nineteenth century — Grimm's Law describes exactly the consonant shift separating Germanic languages from the rest of Indo-European. Apparent exceptions turned out to have their own rules, which strengthened the method considerably.
The most famous confirmation. Saussure argued in 1879 that Proto-Indo-European must have contained sounds that had vanished everywhere, purely because the vowel patterns required them. Decades later Hittite was deciphered and found to preserve exactly such a consonant where predicted — a reconstruction confirmed by a language nobody knew existed when it was made.
What can be recovered beyond sounds. Reconstructed vocabulary implies a culture: words for wheels, wool, horses and honey suggest what the speakers knew, and the absence of shared words for certain things has been used to argue about where and when they lived.
The limits are real. The method reaches back perhaps six to ten thousand years before the signal decays into noise, which is why claims of much deeper relationships are treated sceptically.