The C Major scale seems to be the cornerstone of scales when teaching musical theory, everything I have read about scales so far always seems to use the key of C as it’s starting point.
The reason, I am assuming, is because C Major has no sharps or flats.
Important: The notes for the Major scale are, C D E F G A B
When playing the C Major scale using the 1st pattern of the CAGED system, the scale falls on the open position, which makes sense seeing how the CAGED system basically stems from the open chords.
C
So if we take a look at the scale on the fretboard, you will see something like the following pattern… the root notes are marked with the “X“…
In this example, the thick black double lines represent the nut of the guitar neck.
| $1.0.$2.0.$3.0.$4.0.$5.0.$6.0 || $1.1.$2.X.$6.1 | $3.2.$4.2.$5.2 | $1.3.$2.3.$4.3.$5.X.$6.3 |
Note: In the diagram above it’s the fret numbers that are indicated not the scale degrees, and it isn’t the way you would normally write out a scale using TAB, it’s just to illustrate the fingering pattern of the scale. 
To play this scale, the TAB would look like the following.
Going up in pitch, starting on your C root note, the 5th string 3rd fret, play up to the highest note, 1st string 3rd fret.
| $5.3 $4.0 2 3 $3.0 2 $2.0 1 3 $1.0 1 3 |
Then going back down in pitch, go to the lowest note, 6th string open E, and then back up to your starting C root note at the 5th string 3rd fret.
| $1.3 1 0 $2.3 1 0 $3.2 0 $4.3 2 0 $5.3 2 0 $6.3 1 0 | $6.0 1 3 $5.0 2 3 |
Here is a video that will also help explain everything you have read on this post.