With the C Minor chord it is necessary to make a bar on the first fret and then play the C note on the 3rd fret of the 1st string. The bar made, can either be covering all of the strings on the 1st fret or simply the last 3 strings as the illustration suggests. This chord can be illustrated as follows:
The C Minor chord consists of the notes:
Take a closer look at the demonstration below:
Notice that the difference between the C Minor and C Major chord is simply one note. This is done by adding the A note by marking the 2nd fret on the 2nd string. Differences such as this are important to note as it will facilitate you when having to switch between the C Minor and C Major chords as well as vice versa.