It occurred to me after writing about the impossibility of Universal Translators that, in fact, plausible instrumentation for such things could exist after all, in particular scenarios. To my amazement, I have invented the theoretical blueprints for such a device, at least in principle, and I'd like to share my general design here. Too bad the folks at Star Trek aren't running a contest for the best apologetics to help explain improbable ST props -- I'd score a prize!
First, let's forget about analyzing the spoken grunts and assimilating them into common speech patterns, whether it's during in-person communication or during ship-to-ship contact. A mutual interpreter based on "phonetic roots" is ridiculous, for reasons already discussed. Another crude explanation is based on the idea of brain signals being detected and translated, but this idea should also be dismissed, since it is too akin to "mind-reading" to be permissible.
Instead, let's imagine that most intelligent space critters are plugged into portable translators that are similar to the portable Star Trek units. The functional resemblance of both is not the result of coincidence, of course. The mutual designs arise from a logical presumption that each needs to be taught the other's language. In this basic scenario, the best solution is for both translators to be mini-computers, speaking to each other in a subliminal tongue. The mutual discourse would transpire at supersonic speed, either through radio-like transmissions or subspace. On a conscious level, the human and alien communicators would fail to notice them.
At lightning-fast speed, the mini-computers would transmit data that introduces their linguistic sounds and their meanings until a common consensus of understanding is reached. This basic idea recalls the SETI project in searching for mathematical ideals like pi to establish a mutual language base. The process described here would utilize a technique consisting of linear data to represent a code agreeable to both. (Remember the computers in the Forbin Project? Colossus and its Russian counterpart, Guardian, finding a common dialogue through mathematics? It's a similar correspondence to that.)
It's also like strangers coming together and using sign language to introduce common concepts, along with the sounds associated with them. But the situation proposed here would be MUCH faster, occurring in the blink of an eye. And it would consist of radio or subspace chatter instead of visual sign language and such.
From that point on, it's a simple matter of substituting the sounds of each communicant into sounds the other understands. The mini-computers understand the meanings and emit the vocal phonetics for them in real time.
The only prerequisite, of course, is that both alien species be technologically bright, and armed with the natural foresight to equip themselves with such devices. In addition to that, each race must want to communicate, and must set their translators to open access for that purpose. (Sort of like letting their shields down.)
It's also possible to speculate that most sophisticated spacefarers are trained in a self-made universal quasi-Esperanto language of some kind, based on common assumptions and math codes, prebuilt into the Translators.
Needless to mention, attempting to communicate with a less technological species would run into a brick wall, as discussed earlier.