[RPG] What does Deep Speech look/sound like

The closest thing to an official sound for the drow language might come from TSR's The Drow of the Underdark (1991), which describes some drow vocabulary and phrases. The book describes drow speech as follows:

Drow are as eloquent and musical in their speech as other elves, and are capable of readily reproducing the sounds of other languages. Most drow are good mimics; a drow overhearing speech who imitates the words and tone is 45% likely (+1% per exposure to the language) to be audibly mistaken for the being they are imitating.

According to this, drow sound like elves, and drow adventurers are likely to speak with little or no accent. You can find several elvish language references on Youtube, including J.R.R Tolkien reading a poem in Elvish. Legolas from the Lord of the Rings movies is another good example, although a drow's cultural background would lend itself to a slightly more violent and selfish tone.

In general in play they were ignored or just treated as an abstract language with no further comment.

As to where they came from, here's an answer from Gary Gygax on Dragonsfoot!

As D&D was being quantified and qualified by the publication of the supplemental rules booklets. I decided that Thieves' cant should not be the only secret language. Thus alignment languages come into play, the rational [sic] being they were akin to Hebrew for Jewish and Latin for Roman Catholic persons.

I have since regretted the addition, as the non-cleric user would have only a limited vocabulary, and little cound [sic] be conveyed or understoon [sic] by the use of an alignment language between non-clerical users.

If the DMs would have restricted the use of alignment languages--done mainly because I insisted on that as I should have--then the concept is vaible [sic]. In my view the secret societies of alignment would be pantheonic, known to the clerics of that belief system and special orders of laity only. The ordinary faithful would know only a few words, more or less for recognition.

In other words, it was supposed to be more like religious languages, but wasn't really well thought through. It disappeared in Second Edition and was not missed.