Do they just weld a patch over the hole? Cut out the damaged part and replace it? Or replace the whole panel? Seems like this would not be an easy fix.
And would different armies have their own way of doing things?
You might find this answer by /u/TankArchives about the Red Army interesting.
There are usually a couple ways to repair a tank if there is a hole in it. Depending how the armor was made as well can affect how the repairs are made.
Usually for a Sherman tank the hole was either welded shut if it is small enough or a metal plate was welded on. Depending how shot up the tank is, the tank could be abandoned entirely. You can see pictures of burnt out Shermans but this is due to German tank crews and anti tank gunners hitting the tank multiple times after the crew bailed or was killed. This was to make the tank burn from an ammunition explosion or a gas explosion. A burnt out tank isn’t a tank that can be easily repaired and sent back into the fight. A tank with a single shell through it or a tread knocked off can be easily be repaired.
Now for the Germans they used a process to harden their tank armor. This helped their armor deflect shells better and also harden the armor as well. The metal in the German armor was also not the best quality and it had many impurities and less than average alloys. The hardening process helped offset these less than stellar metals and alloys. However this caused a problem of the armor cracking if hit in the same spots. High explosive shells caused massive holes in some cases. These cracks were usually unrepairable and the tank was written up as a loss.