First they make repetitive sounds (babababa, mamamamama), then they start adding meanings to those sounds (so baba means "bottle", perhaps), then they gradually refine it so that the family no longer has to translate for outsiders.
Here is a video showing a toddler going through the same process learning ASL! An adult helpfully signs the word with a text translation before showing clips of the child's progression using that word between 10 months or so and nearly three years of age. The videos don't start early enough to give us a good view of the babbling stage, though - by the time we see any shots, it's clear what the kid is intending to say. (At least, it's clear to the people in the know!)
Here is a video showing a toddler going through the same process learning ASL! An adult helpfully signs the word with a text translation before showing clips of the child's progression using that word between 10 months or so and nearly three years of age. The videos don't start early enough to give us a good view of the babbling stage, though - by the time we see any shots, it's clear what the kid is intending to say. (At least, it's clear to the people in the know!)