If you're trying to figure out the chords then I would start determining the key, or tonal center, of the song. I was able to determine this song to be in G major just by playing random notes over the song until I hit the one that sounded like the tonic to me.
Once you know the key you can try playing different diatonic chords when you hear changes in the music until you figure out what works. As you practice this eventually you'll start to hear the chords, if you think diatonically there's only 7 possible chords. However in popular music there are a handful of chords which aren't necessarily diatonic that are good to keep in mind. For instance in this song right off the bat I can hear a flat VII major chord, F.
Here are the basic chords to the verse of "A Hard Day's Night" as I hear them:
G C G
It's been a hard day's night
And I've working like a dog