The tune, called "Can't slow down" goes like this:
I've actually been asked to do this a few times over the course of my career and I find it a fun challenge. Here's my working method.
1. Find the form of the piece. If the form is repetitive (as it is in this one), you've saved yourself an awful lot of work. The form of this particular number is:
AABBABABABB
Whew--now I only really have to transcribe two sections and I'll let the copy-and-paste feature of Sibelius do the rest. The next-to-last AB section is faster than what came before it, and the last AB section is faster than that. The first A section is played by violin alone.
2. Determine global parameters. This is a term that Karpinski uses to describe all of the stuff at the beginning of a staff: time signature, key signature, tempo, clef, instruments, etc. This piece is for violin and strings; I'm arranging it for violin and piano. It's in G major and in a 6/8 time signature. The tempo is allegro, approximately dotted quarter = 104 (I have a metronome that you can tap in the tempo).
3. Figure out measure and phrase lengths. I like to do this to create little boxes into which I can drop chords and melodic fragments. In this case, the A and the B sections are both six 6/8 measures long. I'm not sure yet if I'm going to notate the melody across the barline (i.e., starting with an anacrusis) or not.
4. Sketch out bass line and harmonies. In general, the A sections are in the tonic key and the B sections stay mostly in the dominant key. There appears to be some sort of secondary dominant in the B section that leads us into the key of IV. At this point, I'm more concerned with the framework and not the actual bass line. I'll adapt the bass line once I get some of the melody line down.
5. Learn the melody line. Listen to the thing over and over again until you can sing the melody line. I'll probably focus on one section at a time. Again, I'm more concerned with the big picture here: I'll add the fancy little trills and mordents later.
Here's a sketch of the melody and bass lines. Letters indicate solfege syllables:
6. Compare the melody and bass lines. Make sure they add up to the harmonies you hear and make sense with one another.
7. Copy and paste. Once you have the A and B sections notated, fleshing out the piece is as simple as copying and pasting. I like to copy and paste and then I'll make changes to the different iterations of the sections so that it doesn't sound like... well, copied and pasted.
8. Add in details. In a case like this where the music is quite repetitive, I'll try to vary the details as well. I'm not interested in something that matches the recording exactly; rather, as long as the finished product is pretty close (i.e., laymen couldn't tell the difference) and sounds good as music, I'm happy.
I do much of my preliminary sketching and note-taking on paper and only later put it into Sibelius. The computer program, of course, can let you hear what you've written as you go. I'll then send it off to them, probably in PDF format, with a separate violin part and piano score.
I plan to work on this in the next day or two and will post some of my work along the way.