Do I use get familiar with correctly?
John was not familiar with cooking.
After I answered his questions and taught him, he is familiar with cooking now.
So, I helped him to get familiar with cooking.
I think it means
Someone was not familiar with something, and he becomes familiar with that thing now.
Yes. (In another context, 'get familiar with' can have asexual connotation, giving rise to many exchanges such as A: 'It'll give the men a chance to get familiar with their new colleagues.' B: 'Not too familiar, I hope' (the studio audience laughs uproariously). But in this case you're right.)