That's what we're all looking for, isn't it? I think it's the eternal question. I'm probably not the best person to write about this, because it has been something I have always been working on, and it's so frustrating. On second thought, maybe that makes me an OK person to write about it.
First, some history: I jumped into the mandolin and bluegrass with both feet and had to hit the ground running really fast. Not long after starting, I was playing with a bluegrass group composed of people who were way better than me. Then we picked up a fiddler who was really something, especially when it came to speed. Just to hang on, I developed horrible technique: a really stiff wrist, getting speed out of my forearm instead of my wrist and hand. A raggedy, imprecise way to build up speed. Later on, I had to break down and start over. Here's what I've learned along the way:
Speed will come if you work at it patiently. This means playing with a metronome and gradually increasing speed. It's painfully slow and frustrating, but it will come if you work in steady increments. Most importantly, you'll be building up real speed, not the fake speed I went for from the beginning out of necessity.
Most of it is in your right hand and wrist, so keep working on that right hand. That's why everybody recommends you work on the right hand.
Speed is a great way for you to set goals for your practice. Pick a tune or piece you want to master. Find a good recording of it and match the speed with your metronome. Write down that speed, then play the piece yourself at the speed you can play SMOOTHLY. Don't cheat; if you're messing up, slow it down and find your actual speed. Now you have an actual and a target. (Target's pretty far away, isn't it? Don't worry; we're gonna walk ahead until we get closer.) Now use all your good practice skills on that piece, increasing your metronome speed only when you master the tune at each tempo. Slow going, but it will move up. You may never get to the target speed, but you will make progress . And you might surprise yourself and hit the target. (I'm getting into Bryan Kimsey's archery metaphors. Zen and the art of mando archery!)
Scales and exercises are also a great way to increase speed. (All of the above applies.)
Remember to relax! This is incredibly hard to do, especially when you're trying to speed up, because our natural instinct is to tense up when we go for speed. But paradoxically, the tension we feel when we go for speed makes us slow down. So consciously make yourself relax. Relax your hands and fingers. Stop and shake out your right hand. Breathe in deeply and blow out the tension. Be as natural and loose as you can while you play. When you feel yourself tense up, relax again.
Don't sacrifice smoothness and musicality for speed. If it's blazing fast but rough and musically ugly, what good is that? I'd rather hear a tune played a little more slowly but a lot more musically myself, no matter who the player is. You ain't a race driver, you're a musician, and if speed gets to be the whole goal, then you're losing the best part of yourself and the music.
Playing with others (preferably live, but along with recordings if that's all you have access to) is probably the best way to build speed and confidence. You have to keep up! (But remember my sad beginner story and don't let others rush you into bad habits.) When I'm playing with people, I'll push myself to keep up , but if I see I just can't do it, I'll politely back off. Then I'll go home and work on that and hope for better next time.
By the way, many people who can play fast are not so good on slow tunes! You ought to work on that too, and you'll find that they can be just as challenging. A slow ballad or waltz can be just as musically challenging as a breakdown or a mazurka. Ain't music great?