There are two primary ways to cut out distractions. First, we can change our angle in order to change what is behind our subject. Second, (sometimes) we can just move something out of the way - or wait for something (people) to move out of the way. In either case, the goal is to make the background more plain and uniform so that our subject doesn't have any competition for attention.
In the picture below I noticed the colorful toys were distracting from my subject.
So I moved them.
If you have the means, you can remove distractions after the fact on your computer. This is the same image as the one above with a little Photoshop magic: