Howard's advice is very comprehensive. Just oe trick nobody's mentioned is to listen carefully to the final note of a tune. This is usually, but not always. the 'key' note of the tune. You can use this note to identify the key and then you have access to the so called 'three chord trick'. Then, as Taconicus notes you also have the relative minor chords which can, in many places, be substituted for their relative majors.