Smith described the musical construction of his songs this way:
I might think of [an instrument] sort of like a person who, maybe they're talking in the first verse, then in the second verse a new instrument comes in, and they're kind of surprised by that and they have to wait until they've readjusted to this new setting…like they're going 'Uh…wait, I lost my train of thought.' Then they come back later like, 'OK, now I feel comfortable again. (Source)
This approach to music is pretty intriguing, and to show you how it's used in "Miss Misery," we've listed the most important instruments in the song and their purposes in the song below.
Acoustic Guitar
Consider this instrument as the one that represents a clear-headed speaker expressing his true emotions. The only time we hear it very clearly is at the beginning of the song, when the speaker is talking about drinking a lot to be able to deal with his emotions.
Fittingly, just as the speaker tells us he drowns his emotions to get through the day, the acoustic guitar disappears into a flood of new instrumentation.
Bass and Drums/Percussion
Arguably, these instruments play the biggest role in drowning out the acoustic guitar's voice. After the speaker tells us that he's drinking—"the poison rain" being alcohol and "down the drain" being his throat—and will soon be having a darker mindset ("to put bad thoughts in my head"), the bass and drums come in louder than the other instruments.
Because of their traditional description as the rhythm section of a band, we might interpret them as a signal that this drinking-to-forget thing and the dark thoughts that come with it are something of a habit. It's a "rhythm" the speaker has entered into during this confusing time in his life.
These instruments almost never leave the song after their entrance. In fact, the only time both are noticeably gone (with the exception of a very lightly tapped high-hat) is in the verse that begins, "you had plans for both of us." Their disappearance here could be symbolic. The "plans" mentioned in the lyric were obviously not carried out. Mimicking the lack of continuum in the progress of the speaker's relationship, the rhythm section all but disappears, and the song, like the speaker, only has the faintest hint of a driving force behind it.
This point in the song is also the only very specific memory the speaker shares about himself and the girl. The lack of rhythm could be a signal to a listener that the speaker has retreated from the forward-marching present and gone into the past.
Piano
Many of us can call up some image of a singer onstage, sitting on a stool or bench, all alone except for a big, black piano. We just know that whatever is about to be sung is going to sound intimate and confessional.
The reason this image is important is that it could be the exact mood Smith intends to inspire when, just as almost all other instruments disappear, the piano that is elsewhere mixed in the song at a low level becomes the most prominent sound other than the vocals. This is in the same verse mentioned earlier where the singer is lamenting the unfulfilled promise of a "trip out of town."
It seems that the speaker is unable to say explicitly "I miss you, Miss Misery," but this verse is one of the times he comes closest to it. By mentioning this trip that never happened, the speaker is probably saying, "I sort of wish we could have gone on that trip together." Just like we feel that someone sitting alone at a piano is telling us something true and personal, the simple piano line that is the speaker's only accompaniment in this part of the song lends his words a directness and sincerity that may not be as present in parts of the song with a lusher arrangement.
Other instruments certainly join in on this song, such as electric guitar and organ, but the ones above seem to have the most major impact on the song's meaning.