I recently returned from a trip to the above three national parks. I loved working to compose good shots, a task made easy by the trail designers. I've uploaded my recent photos from Grand Canyon North Rim, Zion Park and Bryce in higher res format to to a Flickr album. Feel free to download any or all of these to use them as a screen saver or for any other non-commercial use.
I use a Canon 7D. There are a couple of things I have done here that helped out. One is that I worked hard to compose the photos--I wasn't just snapping pics. This required a lot of hiking, and sometimes climbing off the trail out onto an outcropping. It wasn't dangerous, but I did need to be careful out there This let me get rid of foreground trees, bushes and other distractions. Second, I shot HDR. This means I shot 3 pics of the same scene, bracketing the shutter speed (dark, med, light). I then combined the 3 pics in post-processing with a program called Photomatix, which evens out the lighting. This is amazing software that allow you to approach the HDR with many settings, some of them a bit like a painting,and others straightforward. I then further cropped and straightened and did minor sharpening with Lightroom, another amazing piece of software. Most of these were shot through a new $300 Canon lens that zooms from 18-10mm. That allowed me to squeeze these scenes into one frame, though there is some distortion on the edges at the 10mm setting. Mostly, it was a matter of getting to these places, which required hours of hiking for some of the photos (though others were easy access). I'm about to add the night shot from the north rim at Flickr - it was a long exposure shot where I added foreground lighting in live time with a flashlight. I also obtained the blueish stars by setting my white-balance to tungsten. It involved lots of experimenting, and I did take a lot of shots that didn't work out. That is the main "trick." Don't show people your shots that don't work out well.