Before you change the wallpaper on your iPhone, you need to make sure you have the image you want to use for the wallpaper. You can get that by taking a picture, saving an image from the web or adding photos from your computer. After you have the image you want to use, tap Settings, then Wallpapers and Brightness (Could be Brightness and Wallpaper depending on which iOS your iPhone is running). Then tap Wallpaper.
After you have tapped Wallpaper on your iPhone you will see lists of your photos such as Apple Wallpaper, Camera Roll, My Panoramas and so forth. Tap the list item that contains the image you want to use and then tap the photo that you want to have as your wallpaper. If you chose a photo, you can edit it to set how you want to have it appear as your wallpaper (such as moving it up or down or making it bigger).
When you have finished editing the photo you want for the wallpaper on your iPhone, you can choose to set it as the wallpaper for the iPhone home screen, lock screen or both. Tap which one of these options that you want and the photo will set itself as you prompted it to.
iOS 7 and above iPhone users have an additional option for setting the wallpaper on their iPhones. These are dynamic backgrounds that are animated wallpapers. If you want to use one of those, tap on Dynamic in the Apple Wallpaper section. Keep in mind that while these are attractive, they do take up more battery power to run than a non-animated wallpaper.