I've just got my first DSLR not so long ago and it is downright intimidating with all those controls and all those numbers - but its really not difficult at all after you learn a few basic terms and techniques.
But the first question is what you want to do with your camera?
Option 1: I just want to take OK pictures of the family.
In this case using the auto mode is fine - but you still have to take care of focusing.
The most basic technique is "focus and recompose" - you aim your camera at whatever you want to photograph, press the shutter button half way and hold it there, wait for the camera to focus, move your camera to get the composition you want and only then press the shutter button all the way to take the picture.
Also, you have to make sure the camera is focusing on your subject and not some random detail in the background, there's usually a blinking red dot in the viewfinder or a small frame in the "live view" to show you where the focus is.
You can just ignore all the camera's features and settings and get OK pictures - but the pictures generally won't be better then what you get from a good point-and-shoot.
Option 2: I want to learn about photography and make great pictures
In that care you got to the right place :-)
Basically there are 3 factors that control the picture (Aperture size, Shutter speed and sensor sensitivity) just read about the "exposure triangle" to understand how they relate.
Then take your camera out of auto mode and start to experiment.