The C Major guitar scale in first position is considered a beginner's scale, and is a vital one to know.
We first play the scale in order from the root (C) to the highest tone in this pattern (G), then to the lowest (E), & back to the root (as shown in the tab below).
After we know the scale fingering & can pick it efficiently, then we use the audio file to solo (improvise) using the scale. When we do this, we are studying the way the tones interact with the chords. We focus on what we hear - listening to how tones you choose create reinforcement or tension within a given chord (a harmonic moment).
Playing scales well involves being one step ahead (mentally & in both hands). As we play a tone (a previously planned one), we are planning the next - in the picking (the leave) & fretting hand (the snap).
It's a good idea to memorize the tones of this scale. It becomes a point of comparison for many others. A great way to do this is to say the note name as you play the tones, ascending & descending.
We also practice playing chord scales. A chord scale is playing the chords in alphabetical order, just as we practice scales.