I remember a short story or maybe novella about a first contact. The powers in place bring in a renowned linguist (female, iirc) and her team to help communicate with the aliens.
Working off the aliens' physiology, she works out their way of thinking and representing information. There was some visualisation involved, but they may actually have been studying "spoken" language.
In the end, communication was established and, iirc, the linguist started thinking in the alien patterns as well.
I seem to remember reading the story in Lightspeed magazine in recent years, but I can't find it. It may have appeared somewhere else.
Does anyone have better memory than me?