If you are changing computers and will be using another computer to manage your iPhone, you will first need to disassociate or "unsync" your iPhone from your current computer. It is easy to manage your content manually rather than have iTunes automatically sync things for you such as music, movies and contacts. Manual management of your content is iTunes' default behavior; however, if you have changed it, you'll need to connect your phone to your old computer and follow a few steps.
Launch iTunes on your old computer and connect your iPhone using the USB cable. If your iPhone usually syncs with your computer over your Wi-Fi network, then ensure it is connected to iTunes. Your phone's name should appear in the iTunes menu bar in both connection cases.
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Click on your phone's name in the iTunes menu bar.
Click the "Summary" tab and ensure the check box next to "Manually manage music and videos" is checked.
Click "Apply" to enforce the new setting.