It's definitely important to have your phone set up the way you want it. What kind of device do you have? Is it a widget that you're trying to remove?
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If you are talking about the one on the home screen? You can't. It's not a carrier, or manufacturer choice. Google made it so that if it is removed manufacturers can't install any of Google services.
Which phone do you have. For most android phones, all you have to do is press and hold the Google bar. After a second or two, a trashcan "remove" icon should show up at the top of the screen. Simply drag the item to the trash can and it should be gone.
That doesn't work for the Droid Turbo and Turbo 2; for those phones, long-press an empty space on the home screen, tap Settings, then change the Google Search radio button to Off.