Rule of thumb: "nicht" = "not", "kein" = "no", "not a" or "not any".
- Das ist keine Frau. = That's not a woman.
- Ich weiß nicht. = I do not know.
That doesn't work exactly, but it's a good start. When it comes to your beer example, it is possible to say "Ich trinke Bier nicht", but it's far more natural to say "Ich trinke kein Bier". The reasoning here is that you are stating that the amount of beer you drink is zero -- in English, you could say, "I drink no beer". Think of Nelson's famous quote "I see no ships", which in German would be "Ich sehe keine Schiffe".
- Ich spreche keine Fremdsprachen. = I cannot speak any foreign languages; I speak no foreign languages.
- Ich höre keine Musik. = I cannot hear any music; I hear no music.
- Ich habe keine Ahnung. = I have no idea.