Watch the Exercises Build Chops online guitar lesson by Steve Vai from Alien Guitar Secrets: Passion & Warfare
When I was young, the first thing I learned was exercises. I had what I call "The Vai Advantage": Joe Satriani was my guitar teacher for three years, beginning when I was 12 years old. Joe and me grew up in the same town, and I went to him for lessons every week. I sat next to greatness, watching, learning, and absorbing some of the stuff that I'm passing along.
One of the first things that I started to do when I wanted to get my chops in order (but first make sure to learn a song when getting started) was exercises, going through them for an hour a day. I'll go through some of them here, meant to be played over a metronome slowly, listening to every note until they sound great. When you want to start going faster, make sure you can play slow perfectly and then increase the speed. This is where patience comes in, and being able to pull yourself back when you want to do something overzealous and that's out of your control. If you start overshooting your ability to connect, you're going to sound like an idiot (or, rather, like an amateur).
Coming up with all sorts of exercises is a lot of fun, such as trilling as long as you can in every place possible. It's harder than it looks, especially if it has to sound good! I used to make up libraries of exercises, because it's actually a lot of fun when you can't do something, work at it, and all of a sudden are able to do it. It's my biggest thrill in playing the instrument. So, again: start really slow and perfect, find the right tone, and do exercises until you're blue in the face!