The same way Luke knew in 5 that his friends were in trouble, The Force.
YODA
(shaking his head) Hmm. Control, control. You must learn control.
LUKE
I saw... I saw a city in the clouds.
YODA
Mmm. Friends you have there.
LUKE
They were in pain.
YODA
It is the future you see.
There are also other times when they know things through The Force, like when Vader tells Luke to search his feelings to confirm that Vader is his father, when Obi-Wan senses the destruction of Alderaan, Leah confirming that she and Luke are siblings, etc.
In the Legends stories, it was clear that people use The Force in different ways, so we could have said that Leah had the ability naturally or had developed it.
Now that we only have the movies, we can see that it is an established principle (The Force might tell you if something bad is happening to someone you care about), but we do not have enough details on how The Force works to say for sure if The Force will always tell you, how much you need to care, if you can hate the person for the effect, how easy it is to ignore, how detailed the information is, etc.
As for why Leah and Luke did not comment on the destruction of Alderaan like Obi-Wan, Leah was there and knew what was happening, so there was no point in commenting on it. Since she was not Force trained and in the middle of a traumatic experience, she probably did not recognize The Force. Luke was also untrained and was focused on his lessons.