Is it possible to make the screen show static/glitch effects?

In GZDoom the glitching can be made using glsl shaders, and aplying it to the screen as a post process scene shader (GLDEFS -> Hardware Shaders part: https://zdoom.org/wiki/GLDEFS).

You will also need a ZScript EventHandler overriding the RenderOverlay function to apply the shader, like this (in a ZScript lump):

class ShaderHandler : StaticEventHandler { 
         override void RenderOverlay(RenderEvent e) { 
                 PlayerInfo p = players[consoleplayer]; 
                 Shader.SetEnabled(p, "ShaderName", true); 
        }     
}

The static can be done also with shaders, but more easily you can just stamp a static image in the screen using hudmessage, it allows you to regulate the alpha and all

Im very confused as to what any of that means. Will someone need the Handler and Shaders to play the wad I made it for?

Yes, they will need the handler. 

11 hours ago, ramon.dexter said:

Yes, they will need the handler. 

that helps but i have no clue what im supposed to do or how to approach this. 

So, it's not an easy task. You need a shader code, gldefs definition of the shader code, zscript eventhandler to trigger the shader and optionally a cvar to be able to turn the effect on and off. 

I'm not good at explaining things. Here, take a look at an example shader implementation. In this case, crt effect.

https://github.com/jorisvddonk/GZDoom_CRTShader

Also take a look here:

https://forum.zdoom.org/viewforum.php?f=103