Communication in Star Trek is across many standard channels, and those channels have remained unchanged for hundreds of years.
Think of their communication not so much as dial-up versus high speed internet, but as radio versus digital radio.
Essentially, communication for a space-faring race is easy: You simply send a radio-like signal. Someone (possibly centuries ago) decided upon a standard set of frequencies to communicate on, a standard separation for audio and visual/data signals, and got it agreed to between most major races.
Since then, this protocol has existed. Humans learned it from the Vulcans, and it has spread across the Alpha quadrant. The Kelvin's communications could understand the Narada because they were both using standard, centuries-old protocols.
Even as technology has changed, we retain facets of older technologies. A radio from the 1890s could still pick up today's radio transmissions and play them (in the frequencies it could receive on).
It IS likely that, for example, Federation ships communicate with each other on other frequencies, or using different compression algorithms, or similar - all Federation ships would then have those protocols in memory. That would not, however, keep them from also having the standard protocols.
As for communication with new species, modern ships probably have a software equivalent of the Universal Translator - a bit of software that analyzes incoming signals, selects what is likely video versus audio versus data, and attempts to decode them - likely with the assistance of the communication officer and their department.