The C major scale, along with every other scale on the piano, can be broken down into one group of 3 notes (shown in red) and one group of 4 notes (shown in blue), along with a single note added either to start or finish the scale (shown in green). The alternating groups of 3 and 4 notes can be played all the way up and down the keyboard in succession.
If you look at the layout of the right and left hand, you will notice that the positions are a mirror image of one another.
The following charts will help you visualize the patterns of the C major scale.
Positions and fingerings for the right hand:
Positions and fingerings for the left hand:
This is what the C major scale looks like on the staff. The fingering here is color coded to match your Scale Position Charts.
For a complete and detailed overview of how to practice scales, please read this article.