How do I do the comping ? Do I need to put something green on the computer screen or is it sufficient if II switch the computer off.
Also would it be possible If have shot it real to adjust it afterwards ?
There are a number of ways of doing it. You can cut green paper or felt to size and attach it to the front of the screen and then light that. You can use 2" green paper tape, although then you would have seams, so that works better for phone screens. Or you can simply set the computer to display a solid green or blue field either through the desktop, screensaver, or a photo viewing program. If you do the latter, you will have to watch out for green spill from the screen onto the actor, as well as flicker and rolling shutter issues. You can also just the turn the screen off and add tracking markers for the edges. Since you are doing a VFX shot, it would be helpful to have whomever is actually doing the compositing work to advise you on set during the shoot.
What do you mean by 'adjust it afterwards'? If you shoot the screens for real and decide later that you want to change something on the screen, then you will have to fix it as a VFX shot exactly like the other method. The problem is you may have shot the practical screens in a way that makes it either very difficult or impossible to replace later.
For example, if you shot with shallow depth-of-field and only had part of the screen in focus, or worse, rack-focused through the screen, then that would make comping the screen exponentially more difficult. If you know from the start that the screens may need to be replaced, then you should make sure that the edges of the screens are always in focus. Also, it would be best to avoid out-of-focus objects blocking or moving in front of the screen.
That's why it is best to know exactly what you want and to have the production team agree on how best to achieve each shot in pre-production. Otherwise, you may be shooting yourself in the foot without realizing it.