Obviously you'll want to use more than a cell phone camera to take your photos. Despite the megapixel count boasted by the manufacturer, the size of the sensor and quality of the lens is going to control how good an image you'll be able to produce. Further, the new cameras have software that processes information gathered from the sensor to optimize the resulting image file.
That being said, regardless of whether you use a compact point-and-shoot or fancy DSLR, there's no substitute for good photography skills. The best landscape photography begins with the landscape photographer. Identifying a good subject (and recognizing the best light and angles in which to capture it) and being skilled in composing your photo are the two greatest factors in determining the quality of the images you'll produce.
Some scenes may look good to your eye, but the mechanical limitations of the lens and camera may prevent you from getting a good photograph of them. Or maybe the light isn't right, there are tree branches or other distractions in the way, or you're just too far to adequately capture the scene. Practice is the best way you'll learn these things. Over time I've learned to appreciate some scenes but leave my camera in its bag.
When you do find a great scene, and conditions are right, then it's time to put your skills to use. Choose an angle where the sun is behind you or to one side. Try to avoid large shadows in your scene, especially the foreground. And avoid the mistake that most beginners make, and don't put anything of interest in the center of your photo. Placing interesting objects, including the horizon, off-center (left, right, top, bottom) is the main tenet in the "rule of thirds."
This guideline to great composition says that you can divide your frame into a grid of nine squares, using two horizontal and two vertical lines, and compose your shot such that focal points like the horizon, large rocks and trees, mountain peaks, etc. are placed on one of those lines - or the intersection of those lines.
The reason behind this is that it allows the eye to walk around the photo and is much more pleasing to the viewer than when it's drawn immediately to the center. Try it with some of your shots, and you'll quickly see how well this one rule will greatly improve your landscape photography (not to mention portraits and other nature photography).
