I spent the past hour figuring out the riffs and all from The Root of All Evil. I got those well enough, but when i came to the solo i was stumpted. How can i progress from learning riffs by ear to learning fast solos by ear?
i figured. but learning greenday or something isn't gonna be very helpful

what should i practice to achieve the results i want?
I completely agree with the sing and hum thing. We had a professional brass group talk to our school today that said this exact thing., although I've heard this from everyone ranging from Vai to Santana to most private teachers. If you were to do happy birthday it probably wouldnt take to long if you know a major scale form, and you wouldn't need the recording because you have "internalized" the song. If you can sing the part you want to learn you actually have a chance at reaching your goal of getting it in the least amount of time. If you can not sing the part you wont be able to hear it as well when your trying the "hit and miss" approach. So I would listen to the song (not using for background music but actually concentrateing on it like you would an intense math problem that could win you a million bucks) until you can sing it, once you can sing with the recording THEN grab your guitar and start on the hit-and-miss, I bet you'll grab it much faster, and WAY less rewinding!
There are some great ear training courses that contain exercises like singing along with your playing, playing a chord and singing each of the notes in it etc. I'm currently running through Burge's Perfect Pitch one to see if it works; so far it has actually improved my ear a lot, in being able to separate out the various instruments and notes in a piece.
Yes it is extremely important to sing with the recording. When learning a solo before you pick up the guitar learn how to sing it. This is obviously not possible for parts of a Petrucci solo but sing slower solos and you will internalize them. After doing this your ears begin to open up for more complex things.
Originally posted by arrrgg
When my grandpa comes over to visit, after his shower, he walks around naked to dry off
If you are having trouble learning a fast solo by ear, I would recommend playing your song in windows media player. They have a feature where you can slow the song down up to 50% without changing the pitch. This tool is priceless when learning by ear. there are tons of slow down programs out there that offer a few more bells and whistles, but you have to purchase them. Almost everyone has windows media player on their computers and this is free.

Good luck,
Yes, sing. When I transcribe music, I ALWAYS listen, then sing/hum what I just heard. Everything. Chords, riffs...
Looking at most of the tabs in the net I get the impression most people just play along to a song and just write down whatever sounds in harmony lol

Although of course, at the speed of Petrucci you can't sing it anymore
I use Audacity for slowing down music and isolating parts of music (like a single lick) since it's free.