I have a large hole in my wall by the bathroom shower How can I fix it

I don't know of a video show this, but my Daddy told me to cut out the hole, and then cutting a piece of drywall the size of the hole, then do the mud and tape/sanding. I would bet there is a video on this site or on YouTube.

First off, you have water damage. You need to find the source leak immediately as it can and will destroy the structure if left unattended. Suck it up and call a licensed Plumber and go from there. your house will thank you.

You will have to fix the reason you have the hole in the first place before you fix the wall. (You may need splash guards).

From the picture I suspect there has been water leaking/splashing onto the wall for some time. Depending on what is behind the hole there are a number of ways to fix the problem. Minimum you will most likely have to cut out the area and place a new piece of backerboard in it's place (your local hardware store should be able to tell you how to do that). If you have a lot of dry rot, which I suspect you could have, it could be fairly complicated if studs are also affected, in which case I would suggest you hire a professional to repair the damage, unless you are a handyman or woman. You will most likely also need to paint the entire wall, if not the entire room. Not good news I am sure, but it is something that needs to be done.

I had a similar problem show up shortly after we moved into a (used) house we bought. The former owners had covered up the problem with spackle and paint. I had to fix dry rot behind the shower wall as well as sister in wood alonside the wall studs and a floor joist. If you have less damage than I had you may be able to do the work yourself, but you may be looking at a much bigger problem than a simple repair job.

Looks like moisture from the shower has damaged the wall. You would need to cut out the damage, patch it with new drywall.