caveat - i'm NOT a pro photographer, but in the dim past i was very much into print photography, loaded and developed my film and images as both negatives and positives, did a lot of darkroom work with both b&w and color film, had a gaggle of nikons, canons and other 35mm cameras, all with lenses from wide to telephoto. i've had photo journal article work published in magazines. i'm not an imaging pro, but i know when i'm looking at or taking a good image.
here's just a very few tips ...
1. photography is all about capturing light. if at all possible, keep the light source, if any, to your back, not behind the subject matter's back. if you can't have the light source in front, take great care with backlit subjects!
2. understand your light source. there are two basic kinds of light - large and small.
large light means there is good, diffused light, such as a cloudy but quite bright day where ya can't see much of the sun, if at all. the light seems to be everywhere and little to no shadows. this is the ideal setting for taking potentially great images.
small light means a bright light source (typically the sun), with extreme contrast between brilliant light and very dark shadows. this kinda light is always challenging and much care must be taken positioning the subject and the camera.
2. composition. don't obfuscate the subject - meaning, isolate the subject from the subject's background, so that the subject is the focal point, not the subject and the background. eliminate distractions before snapping the image. in example, move the subject or your camera or both if it looks like a tree branch behind the subject is growing out of the subject's head. this is just good composition.
3. focus, Focus, FOCUS. focus on the subject, not the background!
4. take LOTS of images of the subject! with digital cameras, you get to see the image immediately. do so! check it! digital film is free! take LOTS of images!
5. know your camera. read the manual, learn how it works, take lots of test images in all manner of day light and at night (flash) to see what settings work best for you.
hope some of this helps, and all your trophy shots are great ones.