Unlock your device and navigate to the home screen you wish to remove icons from. You can swipe left or right on your screen to access the different home screens.
Once you are on a home screen which has icons you wish to remove, long press an icon (keep your finger on till the interface changes and do not lift your finger) and the UI should change to show you available options.
Do not lift your finger and look at the options available to you. You may have the option to create a folder, create a new page or remove the icon. The remove icon option is often denoted by a trashcan.
Now swipe your finger to the remove icon option, moving the selected icon to it and the interface should change again. It will either animate the trashcan or make it glow to show that you can lift your finger.
Once the icon is on the remove option (or trashcan) you can lift your finger and the icon will be discarded. You can repeat this exercise for all icons you wish to remove from a home screen.