She somehow learned how to do blood magic to hatch the dragons, she somehow learned how to be immune to fire, she somehow learned how to control the dragons which previously seemed out of control. Everybody is insanely loyal to her, in a series where all of the other characters seem to stab each other in the back. Her only strategy seems to be identify an authority figure and then set them on fire, and then all of their supporters will automatically follow her without question. She doesn't even have any friends, just people to kiss her arse, and if some of them die, she just gets more.
Sounds like you missed a lot.
She didn't learn blood magic, she only burnt a witch and then walked into fire with her eggs. She didn't learn how to be immune to fire, that's a trait some Targaryens have. We know from Tyrion that dragons are exceptionally intelligent, so communicating with them might not be as difficult as you'd think. They recognize their "mother" since they imprint when hatched as was pretty obvious from the earlier seasons. She also taught them commands early on, "dracarys" being one of them.
She inspires loyalty because she is a good person. She kills violent and cruel people, usually slavers or to you a random "authority figure", to free their slaves and in return the slaves adore her. It's really not that complicated. In the case of the Dothraki, they respect strength and bravado, so Dany is right up their alley. She has the strongest claim to the throne, is riding the first dragon in over 100 years, and is a badass. Again, really not too hard to see why she inspires allegiance.
Her handmaidens, Jorah, Ser Barristan, her bloodriders, and Missandei could all be called friends. But it doesn't matter. Having friends isn't a requisite for a good character in this show since almost no one has friends.