I would to do a battle game between two devices.
Can anyone give me some suggest about how to start to learn how to script a player vs player gameplay?
If you know how to code/script… start by figuring out what you need to make it happen. Can you already control a player? No? Make a script that does that. Can he attack? No? Make another script… once thats done try figuring out how you could get players to attack eachother. Some form of collision will probably be required.
Also, I don’t really understand what you mean by “devices”… like two PC’s or Phones? If that’s the case then you will have to play around with networking. Haven’t done that myself (at last not enough to be able to give good advice), but try looking up some tutorials. Only thing I don’t know is if you will be able to release a game that uses networking… or if that was a Unity Pro only feature… assuming that there is no way of getting it done in some other way.
If you do not know how to script or programm. You should start by looking up tutorials… be it text or videos on YouTube. Whichever works for you.
Chances are that you might be able to find scripts that can get you those results, but without knowing how they work there is no real point in using them… so make sure that you know at last something about programming/scripting. 
I want to make a simple ping pong game for mobile devices in which user can play against each one from his own device…
I know how to make a ping pong game but I don’t know how imlement Player vs Player system!!