First time I tried to figure out a song by ear I spent 45 minutes hunting for the first note. Just randomly pressing keys hoping one would match. It was painful.
Now I can figure out most pop songs in maybe 15-20 minutes. Not because I have magical ears but because I learned some tricks that narrow down the guessing.
Find the key first. Most important step. The key tells you which notes are probably in the song. If you're in C major, you're mostly using white keys. Start by humming the melody and hunting for the note that feels like "home" – the one where tension resolves. That's usually your key. Understanding how keys work makes this easier.
Use common chord progressions. Once you know the key, guess the obvious progressions first. I-V-vi-IV (in C: C, G, Am, F) works for like half of pop music. If that doesn't fit, try I-IV-V or vi-IV-I-V. Understanding basic music theory makes this way easier – you're not guessing randomly, you're guessing intelligently.
Melody usually follows the chord. Most melodies use notes from whatever chord is happening underneath. If you found a chord and the melody sounds off, you probably have the wrong chord.
Slow the song down. Apps like Moises let you slow songs to 50% speed without changing pitch. Game changer. Suddenly fast passages become decipherable.
Bass notes are your anchor. The bass usually plays the root of the chord. Isolate bass in the mix if you can, or just listen for the lowest notes. They tell you what chord is happening.
My process: Play the song. Hum along, find key. Listen to bass for chord roots. Try the obvious progressions. Poke around until the chords sound right. Then figure out melody over top.
It's messy. I get things wrong. Backtrack constantly. But it gets faster with practice. And it makes you actually understand the song instead of just copying notes.
For finding sheet music when you don't want to figure it out yourself, MuseScore has free user arrangements of most popular songs.