: Determining the chord progression of a song I've been teaching myself guitar for like 5 months now and by now I know what chords go in what key. The problem is that when I hear a new song, it still takes me some time to figure

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I was writing an answer to this question that was more in-depth, but much of it is echoing the sentiments of Jdjazz, so I will sum up in point form the parts of my answer that overlap with his and elaborate below on the parts that don't.

Mainly:

This is an issue first of ear training and second of experience.
Transcribing is one of the best ways to really focus on ear training. You can make it very easy or very difficult depending on what you choose to transcribe, and the work of transcribing is at least somewhat verifiable (again, depending on what you transcribe).

Transcribing is not, however, what I would suggest to improve ear training if your ear training is at the level where identifying common progressions by ear is foreign/difficult to you. Why? Because by far the most difficult exercise for challenge in ear training, regardless of your ability, is to identify collections of notes that seemingly have no pattern to you. What you likely view now as an issue of ear training (in other words, that you can't hear the chords) is actually a combination of this and your lack of familiarization with hearing common patterns.

When I did ear training in university, we were given largely arbitrary collections of notes (twelve tone rows, to be specific) to identify. This was very difficult, significantly more so than any twelve notes with any kind of identifiable relationship, even if that relationship was obscure. It is my estimation that you are hearing these common chord progressions as if the chords have no relationship to each other.

I don't think you should attempt transcribing right away, as you are likely to find it very frustrating. Rather, I think you should incorporate some basic ear training into your practice regime. Here's three exercises that I like to do and have been doing for years (ear training never stops):

Without looking, play two notes on the piano (or guitar, if you prefer). Can you identify the interval of these two notes? Do this harmonically and melodically (harmonically meaning play the two notes simultaneously, and melodically meaning play them one at a time). At first, this is probably going to be very difficult, and you should stick to notes that are less than an octave apart and you should keep the lower note on the bottom. As you get used to it, however, you should switch things up and broaden the scope of intervals.
Without looking, play a chord on the piano (you can... kind of do this on the guitar but it's very difficult). Can you tell what it is? You want to try to identify this harmonically first and then, if you don't get it, try to do it melodically; this is because identifying chords harmonically is much more difficult than identifying them melodically. This exercise has a lot of potential for adjustment depending on skill level: When you're first starting out, it's a good idea to limit yourself to triads, and as you start to get used to those you can introduce 7th chords and then chords in nonstandard voicings. I tend to separate my hands by a couple of octaves and play four to six notes while doing this. This exercise never stops being useful.
While you're listening to some music and you're away from your instruments, try figuring out what the notes of a melody or chords of a harmony are. If you don't have perfect pitch, you're probably not going to know the key, but that's fine; the point is just to try to guess how the notes relate to each other. Work it out in your head and go slowly; is your guess logically consistent with what you know about melody or harmony? Write it down if you can and go home and test it. Try not to hum while doing this as it makes it considerably easier, but do it if what you're doing is challenging and you're struggling.

I think transcribing is a good way to put these skills to the test once you've learned them, so you might want to make it a goal to transcribe a piece of music you like and want to become very familiar with (...or perhaps too familiar with if transcription goes for you anything like it does for me).

EDIT: I would like to add that I concur that singing is an excellent way to improve your ear training. One of my favorite exercises is to attempt to sing an octave of the chromatic scale without the assistance of an instrument and then checking to see if you made it to the end in tune (sing first note with instrument, next eleven notes without instrument, check last note for intonation). You would be amazed at how difficult this is.

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This is a skill related to ear training. There are a lot of ways to practice ear training, but I recommend developing this particular skill by transcribing lots of songs.

Here's how the transcription process works. Pick a song you like but don't know the chords to. Play the song through your computer speakers. Use a guitar or piano to determine the root of the first chord. As figuring out the root of the first chord, you won't be using your instrument any longer, except at the end to check your work.

Now that you have the root of the first chord, determine whether the chord is major, minor, etc. Try singing an arpeggiated major triad off the root note, and determine whether it matches the sound that you're hear on the recording. If the major triad doesn't seem to fit, try singing an arpeggiated minor minor triad off the root. If the chord contains a seventh, you can sing that note too until you find a match. Once you have your best guess, write out the first chord on a piece of paper.

Upon determining the first chord, move on to the next. Continue listening to the recording, and hit pause once you hear the second chord. Sing the root note of this second chord, and then sing the root note of the first chord. Identify what interval separates the two roots (e.g., maybe the second chord is a fourth down, or a third up, etc.). Use the interval to determine the next root note. Or instead of using the interval, you can also sing up or down the scale until you reach the second root. Then visualize the scale / count the number of scale tones that you ascended/descended in order to determine which note you're on. Once you've found the root note of the second chord, next determine the chord quality (major, minor, etc.) in the say way as before--either by recognizing the sound or by singing arpeggiated triads off the root. Throughout this process, you can un-pause the recording, rewind, and listen back as many times as you'd like.

Repeat this same basic method (of determining chords using relative pitch) until you have written down the chords for a whole section of the song. The length of the section is for you to choose. You could tackle an entire chorus at a time, do an 8-bar phrase, or any other portion you wish. As you gain practice, you'll be able to transcribe the chords for larger and larger sections of a song in this fashion.

Once you have completed the section, check your work using your instrument before moving on to the next section. Don't look up the correct chords online, because checking your work with your instrument is another ear-training exercise. Get out your instrument and play the root notes along with the recording. If you come upon a spot where one of your root notes sounds incorrect, pause the recording, play the root again, loop the recording, and try new notes on your guitar/piano until you've determined the correct root. After you've established the correct root notes, move on to the chord qualities. Play the chords you've written down on your instrument along with the recording to find discrepancies and mismatches. Using your instrument, try to play along and find the correct chords.

Once you've checked your work with your instrument, do a search online to see how you did. This process can be tedious, but it produces real improvement. As you go through it more and more, you'll be able to cut out steps (e.g., determine the root and chord quality together at the same time). Give your level of experience, you might be able to start out by determining the roots and chord qualities together, right from the get-go.

In addition to writing out the chords themselves, it would be immensely valuable to additionally rewrite the progression using Roman numerals. Identify the tonic of the song (the I chord), and write out the scale degree for each chord's root. For example, in the key of Cmaj, an Fmaj chord is the IV chord because F is the fourth scale degree of a Cmaj scale. Doing this will be really valuable because chord progressions are extremely repetitive. This allows you to learn each progression only once instead of in all 12 keys. Your ear will begin to recognize "this is a I-IV-V-IV" progression, and you'll be able to pick up the chords almost instantaneously.

As you'll appreciate, there are specific ear-training skills that this process requires, as a prerequisite to attempting to transcribe a chord progression. Most importantly, one must have (1) a strong ability to identify intervals (distinguish a perfect fourth from a major third, etc.) and (2) the ability to sing arpeggiated chords (major chords, minor chords, dominant 7th chords, etc.).

Performing this exercise with many different songs is likely to produce great results. Attempting the transcription first without your instrument is effective because it trains you to recognize chords by ear without the aid of an instrument. It builds and strengthens your memory of the chord qualities (i.e., how a major chord sounds vs. how a minor chord sounds), which makes future identification quicker.