What are the key objectives when arranging a regular song in fingerstyle?
Timing - make sure you can play the entire song at a steady/consistent tempo. Always practice with a metronome or click track.
Melody - does the song contain a vocal melody? Learn it note for note on the guitar. If the song is instrumental, learn the "head" or the lead melodic part note for note. If you would like people to recognize the song you are playing, being able to play the melody is key.
Tone - I had a guitar instructor who imparted some good advice to me at one point. "Make every note in the melody sound like it is a beautiful jewel."
Harmony - Make sure you know the key of the original song. This will allow you to enhance the melody with harmonies and chord substitutions.
Transpose - figure out if the original key of the song suits an instrumental guitar version. For example can you utilize any open strings or is the melody easier to play in another key?
Natural sounds - I like to play single line notes using open strings when possible. It adds a nice natural sustain to the line. Ringing out notes via open strings is a nice way to tap into the unique properties of the guitar (or instrument similar to a guitar). Open strings make sounds which are unique to the instrument.
The overall objective would be to make full use of the melodic, harmonic and rhythmic opportunities afforded by being able to play several things at the same time. Obviously, there are several 'styles' of fingerstyle. There is the classical approach, the Chet Atkins/Tommy Emmanuel 'Country' style and the jazz, chord melody approach. You may want to stick as close as you can to the original recording or to take some liberties with the rhythm and/or harmony. In any case, you will want to start by learning to play the melody efficiently, bearing in mind that you may subsequently need to move parts of the melody further up the neck to accommodate your harmony/chords. It is often beneficial to transpose the melody into a key, such as E, A or D, that allows you to make use of open strings for your bass part. Some guitarists detune their bottom string from E to D for this reason. Similarly, it can pay to start with open chord shapes where possible. Sometimes these chords are arpeggiated. As you develop, you will probably start to barre some chords in order to be able to fit your parts together. Several styles of music use an alternating root five bass pattern played with the thumb on the E, A and/or D strings. The melody and harmony parts will often sit on the G, B and high E strings and be plucked with the first, second and third fingers, although there are many melodies that may have to go down to the A string. Fingerstyle arranging is a huge topic, but start by making the melody 'sing' then add chords and a bass part.
Here is how I have done exactly this multiple times now.
First, find the chords for the song, either work them out yourself or google them. You have to then find the root note of each chord.
Second, find out the melody of the song and be able to play it in multiple neck positions
Third, this is the step where you put the bass notes and the melody together. You may have to modify the place where the melody is being played and the root notes so you can play them both at once.
Fourth, when you have practiced the third steps a few times, try to find other positions for the original chords which will have the melody position closer to it.
Fifth, try to add in percussive slaps and taps where it will sound good. This will take heaps of time to develop so don't give up fast.
As a first song to try, play hallelujah from Shreck, this song was my first full song and I was able to get to the third step within a week of practice. It truthfully took years to get better and get to the last step but I eventually did it. I first arranged hallelujah at the time when I had just finished learning open chords and was still very uncoordinated. The sweat and time was well worth it when i was able to play a Fingerstyle song well that i had fully arranged.
Good luck :)