This is a great question!

I have actually looked for this before as well. There isn't a huge amount of info I've found but let me find this link that has a pretty lengthy quote about his thoughts.

I found this - it's a bunch of people with some tips and most honestly suck:

http://www.musicthinktank.com/blog/six-steps-to-successful-songwriting-45-tips-from-45-famous-s.html

Here is the Prince quote:

Prince – “Attention to detail – like the right words and notes in the right places – that makes the difference between a good song and a great song.”

Also there is this:

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http://flavorwire.com/306045/25-great-songwriters-on-the-art-of-songwriting

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You can't just click his name - you gotta go thru the whole thing to see what the man has to say. Bastards who made the site. Also - ignore my first post - it looks like the people on that site just took little quotes out of this one.
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Here is the Prince quote included to save you time - although most of them are solid imo on the link I've included here:

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“Attention to detail makes the difference between a good song and a great song. And I meticulously try to put the right sound in the right place, even sounds that you would only notice if I left them out. Sometimes I hear a melody in my head, and it seems like the first color in a painting. And then you can build the rest of the song with other added sounds. You just have to try to be with that first color, like a baby yearns to come to its parents. That’s why creating music is really like giving birth. Music is like the universe: The sounds are like the planets, the air and the light fitting together."

.

“When I write an arrangement, I always picture a blind person listening to the song. And I choose chords and sounds and percussion instruments which would help clarify the feel of the song to a blind person. For instance, a fat chord can conjure up a fat person, or a particular kind of color, or a particular kind of fabric or setting that I’m singing about. Also, some chords suggest a male, others a female, and some ambient sounds suggest togetherness while others suggest loneliness. But with everything I do, I try to keep that blind person in mind. And I make my musicians pay attention to that, too. Like my bassist, Sonny T., can really play a girl’s measurements on his instrument and make you see them. I love the idea of visual sounds.”

[Edited 9/24/16 10:34am]

26ten said:

Also there is this:

.

http://flavorwire.com/306045/25-great-songwriters-on-the-art-of-songwriting

Thank you for this link.

26ten said:

Also there is this:

.

http://flavorwire.com/306045/25-great-songwriters-on-the-art-of-songwriting

.

You can't just click his name - you gotta go thru the whole thing to see what the man has to say. Bastards who made the site. Also - ignore my first post - it looks like the people on that site just took little quotes out of this one.
.
Here is the Prince quote included to save you time - although most of them are solid imo on the link I've included here:

.

“Attention to detail makes the difference between a good song and a great song. And I meticulously try to put the right sound in the right place, even sounds that you would only notice if I left them out. Sometimes I hear a melody in my head, and it seems like the first color in a painting. And then you can build the rest of the song with other added sounds. You just have to try to be with that first color, like a baby yearns to come to its parents. That’s why creating music is really like giving birth. Music is like the universe: The sounds are like the planets, the air and the light fitting together."

.

“When I write an arrangement, I always picture a blind person listening to the song. And I choose chords and sounds and percussion instruments which would help clarify the feel of the song to a blind person. For instance, a fat chord can conjure up a fat person, or a particular kind of color, or a particular kind of fabric or setting that I’m singing about. Also, some chords suggest a male, others a female, and some ambient sounds suggest togetherness while others suggest loneliness. But with everything I do, I try to keep that blind person in mind. And I make my musicians pay attention to that, too. Like my bassist, Sonny T., can really play a girl’s measurements on his instrument and make you see them. I love the idea of visual sounds.”

[Edited 9/24/16 10:34am]

Thank you so much 26Ten!! Those quotes are amazing.

I am not sure there was much writing, Prince has stated many times he heards the songs in his head 'to completion' and then has to try to get it recorded as soon as possible.