Here you can see a diagram of the C major scale. The red notes on the fretboard are the root notes of this particular scale. The lowest string is the low E. Begin from the root note and start building up to the next note on this scale, you either use the same string or use a other string.
3 notes per string
Another way of approaching a scale is with 3notes per stringsystem. Here you can see a diagram of the C major scale. As the name suspect each string contains three notes of the scale. Some guitarist builds 4 notes per string patterns.