How does one hack

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It depends on your definition of "hack", but to hack something like a video game, here are some very general steps you would take, from my understanding of hacking.

1. Have access to the source code of the game, this can be achieved through the disc, usually. Once access is gained, you can begin to probe for unsecured or weak areas, which can be exploited. Alternatively, you could have a list of un-patched exploits.
2. Once you pick or find an exploit, you begin finding ways to bypass areas of the game using it. Such as being able to bypass the area of a multiplayer game that caused you to take damage when hit, and when you found a way to get around this, you can begin exploiting the weakness.
3. When you find ways to bypass areas of a game using an exploit, you can develop tools -or mods- that let you do certain things in the game that are not normally possible (such as god-mode, or unlimited bullets).

However(!), you should be aware that many forms of hacking are illegal, and can be very dangerous to you.