I picked up a D5100 back in July and am just learning how to use it, and I take lots of pictures. Depending on how much time you spend with your camera you should expect it to take a while just to get past the basics of "auto-everything".
Reading is good. The Internet is full of helpful (and not so helpful) information and how to's.
I decided to focus on one aspect of photography at a time and learn that aspect, e.g. how to use aperture priority setting. Play with it, take lots of pictures. Look at the ones you like, what did you do?
BTW non-Nikon batteries may or may not work in your camera, some do some don't, since yours were gifts you can try them out and if they work, grand. I was flabbergasted when I went to buy a second battery ~ $85 on sale! Ended up buying a bundle with a bag and extra's that was on an open box clearance for $50, it included a $85 battery.