Notes:

咱们 zánmen is called an "inclusive pronoun", it means we in the sense of "including you, the person with whom I am speaking". It is used often in the Northern dialects of Chinese. Using 咱们 zánmen correctly will give your speech an authentic feel if you are in Northern China.

我们 wǒmen has both an inclusive "me and you" and exclusive "us without you" meaning. When all else fails, use 我们 wǒmen.

Grammar geeks should note that 咱们 zánmen can not be an object of a verb, it can only be used as the subject of a sentence.