Touch/hold on the application you want to delete. In a second or two all the application icons will start to wobble and will have an X in the upper left corner of the box. Touch the X for the app you want to delete.
Hold your finger on the app until they all start shaking. There will be a small red box with a minus sign on it. Push the minus sign and the app will disappear. It will still be in your iTunes acct if you want to reinstall it. When you are done push the button on the bottom, the apps will stop shaking.
You can also use this to move apps from one location to another. When the apps are shaking, you can put your finger on an app and move it.
Some apps cannot be deleted as they are part of the system.
There are tons of IPhone "How To" vids on YouTube. My 75 year old mother has the IPhone 5. I tried repeatedly to teach her but in the end she learned to use most of the functions by watching videos on YouTube.