practice, x a million, seriously just get your shapes for like major and minor and practice the hell out of em, ive been practicing for aaaaaaages like months and i only just this week have become competant
its not somehting you can learn in a week
Get a metronome. Maybe pick a section of an Avenged Sevenfold song with alot of sweeps in it. Start with a certain downsweep part. Set the metronome rather slow to start with, then speed it up, keeping in time with the metronome. With enough practice, you should be able to get a good amount of speed built up.
Start slow with some simple shapes. I started doing 3 string sweeps on the first 3 strings until I was able to get them to sound out cleanly. Practice 'rolling' your fingers off each string you pick and use smooth down-strokes and up-strokes. After plenty of practice, I can do 5 string sweeps like a mad-man!
Im trying to learn the sweep picking for the song thunderhorse...otherwise i can get the rest of the song
Metronome. Like you i am still learning sweep picking, but i have found that starting out very slowly (80bpm or so) and making sure every note is accurate. I still can't do them as fast some of my friends but i notice an increase in speed everytime i practice them, and mine are sure a hell of alot cleaner :P