Figure out what key it's in. Write it out measure by measure, or phrase by phrase.
Block out the sections first.
If it's pop music, it's probably in a 4/4 meter. 8 bar phrases.
It's a good project for ear training.
Just tap the beat and start writing. Some free software like Audacity can slow it down (I think. I've never actually used it) or "The Amazing Slower Downer" will let you slow down/speed up the tempo without affecting pitch.
Don't believe any chords you find online (esp for free). Even the published stuff isn't always that accurate -- Someone gets paid to crank that stuff out and make it only good enough for someone to buy it. And even if you do have the chords, you don't have to follow exactly what this person performed since you're making your own arranging and are changing instrumentation.
That's how I would start. There's a piano part, a voice part, and I heard some strings.
Or you could copy that other guy, but whatever mistakes he made you would be copying. I would go back to the original source myself.
But you could transcribe the piano part exactly, for whatever you can hear on the recording.
You could get the voice melody. I'm guessing the other guy had the piano part in the left hand and melody in the right. But you don't have to do that -- You could put the melody in octaves or harmonize it or just put it up on octave.
Haha.... And a bass guitar and guitar? Now you have more decisions to make. I would use that other guy for ideas but not necessarily follow him. ... and a synthesizer or two...
And there's your piano technique. If you want to play it right now or create something that's beyond your ability to play.
Or you could arrange it for two pianos.
I think arranging is more about capturing the essence of the piece rather than transcribing it exactly -- unless you have two instruments where an exact transcription will work. I'm guessing you're going more for an arrangement with this -- solo voice with instrumental ensemble to solo piano, if that's what you're going for.
It's just a lot of listening. Lots of going over little pieces. Then resting so your mind can absorb things -- Later on it will sound different and you'll figure things out faster the more you transcribe pieces. Ear training and theory classes help too -- Ear training is doing dictation/transcription like this but it would be something like working with the just the melody or chords. Nothing this complicated (at least I didn't but we had to transcribe some things). [Ear training also has some sight-singing, the reverse of dictation exercises -- see it on paper and sing it or hear it in your mind.) Knowing music theory means you can think about what should be according to the rules of music theory.
This sounds like a standard pop piece though -- It's probably all tonal. Begins and ends in the same key. Alternates between A and B sections. I didn't hear if there was a C section. Builds up to the end. Things like that.
Topic: Have a song but cannot find sheet music