Whenever you might need to "crack" a wireless network, the task is about cracking the encryption, authentication or hash algorithm to derive some kind of secret password.
There is a bunch of ways you may achieve it −
You can try to break the encryption algorithm with the weaker ones. It might be doable, but to be very honest with you, now-a-days no one would use the algorithm that may be breakable, therefore, unless you are a high-class crypto analyst that would not be the way forward.
Most of the approaches would concentrate on using some kind of dictionary or brute-force attack.
Just to give you a simple idea of how this attack may be performed, imagine we have some password that "we don't know" - "MySecretPassword". In some way, we got into possession of MD5 and SHA1 signature