Chances are if you have a decent DSLR camera, you're only comfortable in 'Auto' mode. Perhaps you've tried to use 'Manual' mode because you think you should, or a pro tried to teach you how in 2 hours, and it didn't work out - and then you couldn't get your camera back to 'normal'. Never fear, there is a mode that requires minimal camera knowledge, but gives you gorgeous pictures - 'Aperture' mode. I used this mode for 3-4 years before I was able to easily transition to manual - after I'd become limited by 'Aperture's capabilities. The aperture controls the depth of field, and it's the MOST IMPORTANT feature of a picture that 'Auto' doesn't even let you adjust. It's the sole reason you should get out of Auto and into Aperture mode, now.
The aperture is the variable-sized opening through which light passes, it controls the 'depth of field', and the 'depth of field' refers to how much of the picture is in focus, e.g., whether the subject is in focus and the background is blurry. For pictures that really stand out from a cell phone snap, controlling the aperture on a DSLR is what makes the difference. The smaller the aperture number, the larger the opening, and the blurrier the background. I know instantly whether an image was cell-shot or DSLR-shot by the depth of field alone. Cell phones just can't do what your DSLR can, and sadly, most DSLR owners can't take advantage of it.
Aperture mode requires you to adjust just 3 settings: ISO, white balance, and the aperture, and the camera does the rest. You can even opt to have 2 of those 3 settings (ISO and white balance) handled automatically by the camera, especially if you're just getting out of Auto for the first time. For the record, ISO controls the sensitivity of the camera's sensor, low ISO (100-200) for bright outdoor light, and high ISO (400+) for indoor images. Similarly the white balance controls the 'color' of the light in the image you create - indoor incandescent lighting looks orange, flash lighting looks bluish. The proper white balance setting will make the light look natural. But you're going to leave those 2 on auto, which means you have just one thing to adjust: the size of the opening that light passes through. Easy!
In Aperture mode, you simply set the aperture number. The smaller the number, the larger the opening, and the blurrier the background. E.g. your little girl is sitting in front of you in a field, you set the Aperture to it's lowest number, and in the resulting image she stands out as your crisply focused subject, surrounded by softly blurred fields. Or another example: your son's class is lined up to march in the school parade, you again set your aperture number as low as it'll go, then focus on your child. Then he is the ONLY person in focus, and stands out as the subject of the picture despite 15 other kids lined up with him. Conversely if you're taking a picture of a house, you want your aperture to be a high number, so as much of the house and landscape is in focus as possible. Frankly in that situation, I grab my cell phone ;)
There are a few other intricacies to learn, because a high aperture number = small opening = less light for the camera's sensor, which can result in a looong exposure and human hands just can't hold a camera steady enough. Solution: tripod or flash. Similarly in bright sunlight the lowest possible aperture could let in too much light, and the picture will be 'blown out' and way too bright. Solution: Raise the aperture number, or use a 'neutral density filter'. With practice you'll quickly realize the limits of your camera and will find ways to compensate.
A caveat, pictures in Aperture mode tended to be slightly underexposed, at least they were for me. But even the simplest photo editing software can handle the exposure adjustment for you should you wish. So give it a shot, and enjoy the jump in picture quality. Not to mention the satisfaction of finally getting your money's worth from that expensive camera!
Happy shooting :)