Here is the C scale pattern:

See how the open C chord pattern fits right in (take special note of the root note "R").

The scale pattern is on the left and the the open C chord is on the right.

To practice play the open C chord and then play the scale pattern, or any other way you want to play it. Practice it over and over until you've got it memorized.

Here are a few riffs I put together using the open C chord with it's scale pattern. Notice how everything seems to gravitate to the C chord, or at least the root note?

Now that you've seen my examples, see if you can come up with your own! This will help you to solidify the pattern in your mind.