A scale diagram is different from a chord diagram. Instead of showing one shape with a few fingers pressed down, it lights up every position on the neck where a note from the scale lives. You'll usually see two or three dots per string across the first twelve frets, and those are the only places the scale notes appear.
The root note (the scale's home pitch) is highlighted in a different colour from the rest, so you can see where the scale's tonal centre lands. In C Major, for instance, every C across the neck is marked in brick red while the other six notes of the scale (D, E, F, G, A, B) appear in olive. Press any lit position and you're guaranteed to be in the scale.
Reading the diagram works the same way as reading a chord: the four vertical lines are the strings (G, C, E, A from left to right in standard tuning), the horizontal lines are the frets, and the thick bar at the top is the nut. Open strings sit just above the nut. The numbers along the bottom mark important frets (3, 5, 7, 9, 12) to help orient you.
Scales repeat every twelve frets. The pattern of dots you see in the first twelve frets is identical to the pattern from fret twelve onward (just shifted up an octave), which is why most scale charts stop at the 12th fret marker.