I think the simplest way to answer this is that historians have to start engaging much more with the archaeological material, and therefore the interpretations of archaeologists, than they may otherwise have done.

I am particularly interested in ancient Roman interactions (and usually conquests) with different societies and many in the west, such as the Gauls, Germans and Britons, did not have written language tradition.

In the absence of literary sources, historians investigating these periods are left with some Roman textual references and the archaeological material.

In the case of the Roman sources, these can provide a useful perspective on military campaigns, and how the Romans viewed and interacted with native peoples. Caesar's Gallic War and Strabo's Gerography are two such examples. But, as you can imagine they often give a biased or misunderstood 'outsider' perspective on how native people actually lived and how their societies functioned.

Therefore, we can turn to archaeology and study the material remains of the people themselves. This comes with its own Pandora's box of problems such as the survival of evidence and the interpretation of the modern archaeologist. But it does mean historians can cross reference what the (in this example) the Roman sources claim about the societies, with what the archaeologist have proof for. For instance, Strabo records the resources that were available in Britain at the point of first Roman contact:

“he [Caesar] found the corn in the fields. [… Britain] produces corn, cattle, gold, silver, and iron, which things are brought thence, and also skins, and slaves, and dogs sagacious in hunting” (Strabo, Geog. 4.5.1)

All of which can be cross referenced and verified in the archaeological record. However, Strabo's other claims such as:

“The Britons, since they are man-eaters as well as heavy eaters, and since, further, they count it an honourable thing, when their fathers die, to devour them.” Strabo, Geog., 4.5.155-156

Hasn't got as much to back it up in the archaeological material, so can be said to be a far more dubious claim.

In terms of actually leaning a language that is not only dead, but had very few or no written forms is a whole extra ball game. For languages, like you mentioned, that we have a written source for, but no way f reading it, the are often deciphered after the discover of multi-lingual texts. This was the case Behistun which was part of a remarkable translation of Old Persian, Babylonian and Elamite by Georg Friedrich Grotefend in the 18th century and then Sir Henry Rawlinson in the 19th.

This is the same as the translation of hieroglyphics using the Rosetta stone whereby the unknown language can be (painstakingly) figured out from the known ancient languages below, based on the premise that they say basically the same thing.

But what about languages that don't even have inscriptions? To go back to the Romans and the Britons that I mentioned above, it is in theory possible to trace linguistic traditions back from more modern 'child' languages. These include Anglo-Saxon, Norse and Celtic. In such cases old language traditions such as Goidelic languages (Irish and Scottish) Welsh and Cornish languages can be traced backwards to provide an indication of how these 'very dead' languages may have been spoken.

A strong proponent of this thinking (in the UK) is Raimund Karl, who would be worth a read if you wanted to explore the 'Celtic' languages more.

(see: Karl, R. (2008). Random Coincidences Or: the return of the Celtic to Iron Age Britain. Proceedings of the Prehistoric Society, 74, 69–78.) Or if you wanted to know why people think that languages just can't be used in that way, check out the work by Collis:

(Collis, J. (2011). “Reconstructing Iron Age Society” Revisited. In Atlantic Europe in the First Milenium BC: Crossing the Divide (pp. 223–241). Oxford: Oxford University Press.)

Karl and Collis have something of an intellectual and academic rivalry so rebuff articles are common!

If you want to know more about the use of archaeology for the study of pre-literate societies, the BBC series by archaeologist Neil Oliver is really quite good and has a section on languages (which I can't find now, but it is definitely there.

Another route in is through linguistic stratigraphy. Although such approaches are controversial to some historians, historical linguistics is actually quite rigorous in its practices in many cases. Such broad and rough techniques as glottochronology -- by which language splits are dated by number of differing words -- have largely been rejected, whereas cognate analysis in the context of broader changes within specific languages seems quite well supported by data.

Some of the best examples of these techniques being used in meaningful ways come from African History. Chris Ehret, for example, constructed a history of social and economic change in sub-Saharan Africa in An African Classical Age. I have been even more impressed by Kathryn de Luna's work. She took on one of the hardest histories to get at through any source -- emotion -- in her article "Affect and Society in Precolonial Africa. She gives two large examples. In the first, she studies the broadly shared Bantu root -kumu, normally translated as chief. Looking at the Krobo Okumu (priest with claim to authority), Tumba nkumu (an alternate to the owner of the land) and Chiga omufumu (ritual specialist who accrues honor and gives it back) she explains changes over time from root Bantu societies to successors. In particular, she argues that the Tumba nkumu developed as a way of building community integration and sense of self outside of rulership, as the nkumu figure worked hard to earn his position and the community supported him, meaning that his eventual elevation conveyed honor on all.

Another example she gives is the development of the term longo/mulongo among Ila-speakers, who borrowed it from Kusi speakers who used the term to mean brother. Over time, it came to instead mean "fictive kin" and formalized friend. de Luna argues that this was part of the process by which the immigrant Ila found ways to share land and establish partnerships with the resident Kusi, and helps explain how conflict was generally avoided through peer-to-peer close relationships.

These are two good examples, I think, of the kind of work that historical linguists can contribute to reconstructing the past before/without written languages.