One of the most common questions I see is, "what's the best way to transcribe?"
Short answer: There is no best way. Just do it.
Far too often we get so caught up in the How that we never actually get to the Doing. My advice is to just do it. Get out there and transcribe. No matter how you go about, you will benefit.
As far as the benefits, there are many depending on how you go about transcribing (improved sight-reading, better intonation and tone, better technique, expanded vocabulary...)
When I first started transcribing, I wrote everything down as soon an I learned it. I would regularly go back and read through what I wrote. My tone and intonation improved, and some language sunk in, but not as much as if I had memorized the piece. An unexpected benefit was that my ability to sight-read increased dramatically! This came from writing it down.
My current approach is to memorize the piece, and write it down afterwards (oftentimes from memory and without a horn). I feel this is the "best" way (for me, at least). I still receive the same benefits as before, but now I'm really letting the language sink in to my subconscious.
No matter how you go about transcribing, it doesn't really matter, just as long as you are doing it. Transcription books are great, particularly for those who have transcribed and listened a lot on their own, but they are no substitute for actually doing the work yourself.
As for programs to help with the transcription process, I have used the Amazing Slow Downer and Transcribe. Both are great. There are some who advocate that you shouldn't slow down the music, but try to learn it at tempo. Developing this ability can really help you out on the bandstand when you have to learn a tune by ear on the fly. I always try to do this first, but more often than not I end up slowing the music down a little.