How does the crack of a PC game/software work?

I'd first like to say this is purely for educational purposes. When I was learning assembly, I was tinkering with apps, and found a debugger to debug the programs, it was called as OllyDbg.

I accidentally learned that I could crack apps using it, and to test my idea I did crack an AntiVirus program, and it worked. This is only one of the techniques and here is how it's done.

The app that I cracked came with two modules, files called as avEngine.dll and activation.dll
I opened the activation module in OllyDbg to find the assembly code like this in the .text section.

section .text
:checkActivation
push ebp
mov ebp, esp
...
...
call validateCode
cmp eax, #1
jne activationFail
...
... ; Code on successful validation
...
jmp endCheckActivation
:activationFail
...
... ; Code to show error message
...
:endCheckActivation
pop ebp
ret

As you see, there is a command after comparing, called as jne which stands for jump if not equals. What should I do if I don't have the real activation code?
I just modified the instruction, from jne to je saying that I wanted to execute the failed code when it succeeded. I saved the assembly and replaced the original file, and opened the app. I entered a random shit and it turned to Pro version.

Things however might not be this simple always. There will be a ton of other checks. You might not get these labels to understand what is what. I got them because I was trying a debug build. This is also a single technique, there are a lots of them real crackers use.