Nicola,
I think the easiest way would be to hold down the first fret, and slide up to your last fret (22nd, 24th, whatever your last fret may be) and every time you move from one fret to another, play the note. For instance, place your finger on the E string at the first fret, and slide to the 2nd fret, then play the second fret. Then slide to third and play the third, and do this until you can smoothly and quickly slide up the fingerboard and get all the notes in. I hope this helps.
Joey

Just a small tip: always keep your thumb (left hand if you play 'normal') behind your middle finger (on the other side of the neck) and keep playing in the same position as much as you can.
Don't put your thumb over the neck's top. It decreases too much in speed.

ROnnie