This is a skill that I've taught, as a piano teacher, to many many students. There is an exact approach that you can take that works with a large subset of pop songs; I refer to pop in the most general way as any styles of music that are currently popular.
Here are some of the approaches I use and teach. We're going to take "Closer" by The Chainsmokers as an example throughout. I'll use "ex)" to indicate when I'm referring to how I would use a technique with that song.
Bass Line Approach
The bass line is one of the most important factors in learning how to play songs. For the majority of the time, the bass line is the root of the chord.
1. Determine the key of the song. This always has to happen first, so if you already know how to do this, then this is ALWAYS the first step. For those reading this post that might not know how to determine the key, here are the steps:
- Choose one or two parts of the song (I'll use the intro and verse of "Closer"
- Play the song and try to identify at least 4 or 5 different notes played by instruments or sung by a voice
- ex) I heard an F, Ab, Bb, C, Db and Eb when I played "Closer"
- Use music theory about keys and key signatures to narrow down your key options (I'll approach this as looking at major keys only for simplicity)
- ex) since we have 4 flats that we know of, the key might be Ab major (4 flats)
- ex) we're missing a G, so it could be G or Gb, which means that the key could be Db major (5 flats)
- play the scales for the keys you've determined when the song is playing...one of the options should "sound" best
- ex) Db major sounds a little bit off, but Ab major sounds like it fits
- ex) From experience, some students find this part easy and some can't hear the difference between the two scale options
- listen to the song for at least 20 - 30 seconds (this helps your brain establish the tonality of the key)
- try singing a well-known children's song like "Mary Had A Little Lamb" while the song you're trying to figure out is playing
- "Mary Had A Little Lamb" starts on the 3rd (mediant) note of a major scale
- the third note of "Mary Had A Little Lamb" will be the tonic of the key
- ex) when I sing "Mary Had A Little Lamb" over "Closer" by The Chainsmokers I see that my third note is Ab, which is the tonic of the key for the song
- if you don't want to use "Mary Had A Little Lamb" because you don't know the song, try "Happy Birthday" and the key will always occur when you sing the word "you"
2. Find Chord Lengths. If you have a good grasp on notation, then write out how long each chord is played for. In most pop music, this will be 2 beats or 4 beats. This step will help you figure out when chords change. The tricky thing is identifying how many chords there are and this usually comes with practice.
ex) I noticed that the first chord in "Closer" was 2 and 1/2 beats. The second chord was 1 and 1/2 beats. The third chord was 2 and 1/2 beats and the fourth chord was 1 and 1/2 beats. I've determined that there may be 4 chords because it seems to repeat after these 4 chords.
3. Identify bass notes. This is the most crucial step. As stated before, the bass instrument will usually play the root for the lifetime of the chord. Some people are incapable of hearing the bass note because their "ear" has not developed enough. This can be fixed with lots of ear training.
ex) I hear a Db for 2.5 beats, then an Eb for 1.5 beats, then an F for 2.5 beats, then an Eb again for 1.5 beats. In the key of Ab, we have the following chords: Ab, Bbm, Cm, Db, Eb, Fm and Gdim. If I'm hearing a Db in the bass line for the first chord, then it's going to be Db major most likely. I hear an Eb next, which means the chord is Eb major. Next I hear an F, which means the chord will be F minor. Lastly, I hear another Eb, which means Eb major. The chords are NOT just plain-Jane triads, they have 7ths and 9ths in them as well, but this is beyond the scope of this answer.
Note: There are many songs where certain bass notes do NOT represent the root of the chord. Usually in these cases the bass note is still part of the chord, it might just be the 3rd or 5th of the chord instead of the root.
As stated in securehope's answer, the melody of the song can be useful in determining the chords for the song, but I don't believe it's the best way to identify chords and here's why:
- the melody note that you hear at any given time may not be in the chord
- the melody note may be a "passing note" or "appoggiatura", both of which are known as non-chord notes
- the melody note may be an extension of the chord like the 7th, 9th, 11th, 13th which will make identification harder if you don't know your theory very well
Don't get me wrong, if this approach works for you, then it's a great approach. I'm just stating problems that I've had with my students using this approach exclusively.
For any of these approaches to work, you need to have a strong foundation in basic musical theory, which means you need to understand how key signatures and keys work.
As stated by securehope, learn the "number system". This is the a system where you take the 7 notes of each scale and assign them a number from 1 to 7, but with Roman Numerals. For example, the scale for C major is CDEFGAB. The chords for C major use those notes exclusively. There are no sharps or flats in any of the "native" chords for the key of C major. The first chord starts on C and it's C major, known as the I chord (pronounced "one chord"). The ii chord is D minor (lower case for minor chords, upper case for major). The iii chord is E minor. The IV chord is F major. The V chord is G major. The vi chord is Am. The vii chord is Bdim. The reason that knowing this is so important is that it allows you to play in any key. If I know that "Closer" by The Chainsmokers is in Ab and that the chords are Db, Eb, Fm, Eb, then I can codify the chords numerically. Db is the IV chord, Eb is the V chord, Fm is the vi chord. So if I want to play the song in the key of C major instead, then the chords would be F, G, Am, G. There are a ton more applications of using the number system. It's absolutely fundamental to everything I do. Here's a YouTube vid I put out on this concept.
Lastly, ignore intervals for the most part, I have not found them useful in identifying keys or chords. They are important as a theory concept for building chords, but that's about it.
I know how frustrating some of this stuff is. I struggled with it to when I first starting learning music. Hope this helps!