While the C major in open position should be no sweat to you by now, the barred version is a little more challenging.
It’s hard to get at first, but don’t you dare skip it. It’s important know this shape.
C Major Open
C Major Barred
(audio example is C#/Db root note on the 4th fret)
You can determine the name of the chord when the root (lowest) note is played on the frets in the chart below.
If you’re having trouble with the fingering on this one try practicing the fingering for the open C major chord like in the diagram below (picture on the left). Then play it barred (picture on the right) on the 1st fret, then the 2nd, and continue up the fret board all the way up to the 12th fret. Then go all the way back down to the open position.
The exercise is performed in the audio example below the diagram.