I'm new to Arduino, I want to use Arduino and a mobile phone screen to make a simple touch board.
This phone screen I mean, is like this:

Can I connect it to Arduino, and when my fingers touch the screen, Arduino can get the events?
First, find a suitable phone screen! Good luck. Most of the touch screens that I have found are resistive, and will never feel like an iPhone. Try googling "Arduino touch screen". Adafruit have a promising one.
Once you find your screen, you will need to interface to it. With luck it will come with a pre-built library. Otherwise you will be up for quite a lot of coding.