One Finger Per Fret, Up And Down
First let me show you a very common exercise that's good for your single-note technique. Remember that it's not supposed to make sense musically. It's purely a work-out for your fingers.
This exercise starts with your 1st finger in the 1st fret of the low E-string. Then we'll grab the 2nd fret with our middle finger. That's followed by the 3rd fret with our ring finger and finally we have the 4th fret with our pinky.
Now in our right hand we'll go down, up, down, up, repeating. After this we'll do the same thing on the next string. And so on.
Make sure you're using your finger tips. Make sure your fingers aren't flailing all over the place. If any of that is tricky, you just have to slow it down.
Once you're ready, try doing it backwards. This exercise is good for your left and right hand coordination and it forces your pinky to be a part of the team. Otherwise it has a tendency to try to avoid getting involved and that's a shame cause it's quite useful to have it ready.
This is sometimes referred to as spider fingers or the spider fingers exercise.
Now let me demonstrate this for you. You're of course welcome to try playing along with me, but the best thing is probably to watch my demonstration and then try it on your own afterwards so you can find your own tempo.