Move around: even if you think that the best shot is from a specific position, experiment with shooting angles and move around the subject to find the best focus point.
Determine your frame: your subject will most likely be surrounded by other elements, such as trees, sky, and other objects. If your framing element (like sky for example) is too bright, dull, pale or simply distracting to the eye, you might want to reduce the amount of framing element. Move closer to the subject to capture less sky, while still maintaining it as the frame of the picture.
Maintain a Theme: if you are photographing natural subjects like insects and birds, incorporating an urban element such as concrete or metal will most likely not benefit the essence of your photograph. Unless you are looking to capture the contrasting qualities of both elements, you are better off keeping to a theme so that your picture keeps order and the eye finds a logical way to read/interpret it.
Explore New Boundaries: if you are used to using the sky as a means of framing most of your pictures, try something new to add dynamicity to your photographs.
Photograph a subject under an intricate doorway for a different look, or use another object or set of objects to draw the eye to a specific part of the image.
Don’t Overshadow the Subject: while a bright color is always pleasing to the eye, it can draw attention away from the subject, completely throwing off the balance of the photograph. Select framing elements that accompany the theme of the photograph and complement the essence of the subject without taking away from its importance in the picture.