if it is the key of no sharps and flats---look at first chord, look at the last chord, and especially look at the last four measures.
if the last two chords are E7 and Am (and any chord extensions or alterations), then it is a good bet it is in A minor. if the last two chords are G7 and C (and any extensions, etc), then it is most probably in C.
if there are many instances of F# and G#, that also is an indication of A minor.
natural, harmonic, melodic are not three different keys, just different forms of the minor scale. so, if you determine that it is in A minor, and no F#'s or G#'s, then natural minor is the predominant sound. (unlikely). if there is F natural and G#, then harmonic minor is the sound (several tunes exploit this sonority). most likely you will find F#'s and G#'s, as well as the natural forms of both notes, which is by far most common, and will indicate the melodic minor sound.
rarely, it may be in minor and have F# but G natural, a dorian sound.
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