1. You can move. Try a different angle, move up, crouch down, move left/right, see if a slightly different point of view removes the distraction. Try zooming in or moving in closer, sometimes that is all you need to do.
2. If the distraction is small, like a piece of grass, a weed or something you can move, you can physically remove it. Clothespins are wonderful for pulling weeds, grass and other small items out of the way without damaging them.
3. You can try a larger aperture or a longer focal length to blur that distraction. If your camera has a Depth of Field preview button, use it! Experiment with aperture selections until you find one that gives you the depth of field needed for your main subject, but also creates blur where needed.
4. If you are shooting a close up, you can substitute a new background. You can use fabric, foam core, cardboard, an out of focus photo printed in a large size... the possibilities are endless. The blue background in this spider web shot is my jacket, it's hiding a background full of lines that drew attention away from the web pattern.
When shooting flowers, I sometimes choose the background before I pick my main subject. A blast of color in a flower garden can catch my eye, and then I just need to chose a subject and angle that incorporates that background into my photo. If there isn't anything nearby I can use as my main subject to take advantage of the background, I sometimes add my own. For the image below, I used a daisy I'd brought along on my morning walk, I just clipped it to a tall stalk of grass with a clothespin and then made this photo.
Here are some other shots I made by choosing my background first:
Paying close attention to the background will make your photos much stronger, try it and see!