My character picked up the Deep Sage feat, so he can now speak, read and write Deep Speech. But I haven't been able to find any published examples of what it may look like when written or sound like when spoken.
This thread implies that Deep Speech uses the same alphabet as Elven; namely, Rellanic:
I know of no standard accepted guideline resource for fictional languages. There are accepted forms for fictional languages like elven, dwarven, Klingon, etc, but for many it is up to the group to define.
I would say get together with your DM and the group and come to a consensus on it. It could be guttural or lyrical. It might be a whispered language with no body/facial movement by virtue of being in an underground environment.
I would say get creative and have fun with it.
Some research leads me to believe there's no real "correct" answer here. That said, if you want to make up something on your own, I'd suggest using Google Translate and picking one of the obscurer languages. You can use the translated text as examples of the writing, and click Listen to hear it spoken.
I would describe it like the slow grinding of words upon each other, like that of one tectonic plate upon another with a ponderously slow cadence and a grinding intensity that flares into heat from time to time when the social friction becomes the greatest.
So less focus on actual pronunciation, but more on the evocative nature of the spoken word.
(This is just my own idea and I do not know of any written support of it.)
Our group always thinks of deep speech as a high pitched screechy chittering gibber. Primordial and abyssal are gutteral and deep and downright imposing. Supernal is more musical and flowing and almost sounds like mellow tones of soothing instruments (we say the instruments were modeled after the voices of the gods.) Which leaves the far realm, the source of all these odd, gibbering screechy monsters that just dont fit with their surroundings. An aboleth may have a much deeper resonance and thus sound more gutteral but it still is a rapid sequence of gibbers clicks and screeches. While a smaller abberant creature will have a much higherpitched "voice", sometimes so high it cant be heard. Thats just how our group runs the more unusual languages and how we think of them. We dont give Deep Speech a written form concidering the fact that the speakers usally come from the far realm, and most races that speak it also speak common unless they are aberant. This makes deep speech memorable and easy to run, No deep notes being passed, no deep secret letters to the king and its hard to not be unnerved by a 4 story monster screaming like a girl at you threatining you in its language.
Writing in deep speech exists in the fourth dimension, and it is not written but summoned into our dimension, which basically is why it breaks everyone's mind. at least that's how I always interpreted it. Speech of deep speech, is more like a deep constant tone with maybe some gurgles and the like inserted in. the idea is that deep speech is mostly a language of the mind, breaking the minds of those not used to it and those who understand would pick up meaning not heard by people who don't understand the language.