How can you tell what key a song is in, example, how would know what key Nothing Else Matters by Metallica is in?

And R.I.P. Samantha
^ yes but that doesn't define the key (other than its in E, is it E phrygian? E major? E minor? E lydian?) and to help you out RTFS, it tells how to figure out keys. if you still have questions lemme know, its pretty easy once you get the hang of it.
Keys are a tricky thing because there is no method that works 100% of the time. The key of a piece refers to the passage's overall tonality, as in the note that seems to play the role of the tonic. This note is the one that brings a feeling of consonance or rest to the music, where as the dominant or leading-tone bring tension.

So in order to figure out the key of a piece, you must determine which note is the tonic. This can be done by looking for fragments of major or minor scales within the music, and using accidentals to judge which key fits best. This method can be misleading as many pieces use passing tones and modulations which might throw you off. Another indicator of tonality are cadences and chords. If you see and hear a perfect, plagal or imperfect cadence, you will know the tonic. Dominant seventh chords often play a role in perfect cadences, and may tell you which note is the dominant, revealing the tonic. Another thing to note is that pieces which include a raised submediant and/or leading-tone are most often in minor keys due to the harmonic and melodic minor scales that are so commonly used.

You asked about Metallica music, in which case most of the above won't be required, as this music is fairly simple. Just look at the chords they play and you should be able to spot the tonic.

Good luck.
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I'm pretty sure nothing else matters is in E minor. When your first learning to train your ear, it takes a long time to get used to it. But if you know the major and minor scales on your instrument, just listen to the song and try out different scales until you find one that sounds right. Do that enough times, and you should be able to at least tell the difference of a major and minor key just by the sound. Just finding the root note is the part that can take a while.
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dude calebrocker, that first song on your list almost made me cry
you win my good sir

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