The C major chord requires a bit of manual dexterity, as you have to stretch your fingers across the fingerboard. The A major chord can also be tricky, but there are multiple ways to play it. You may have noticed that you don't strum all six strings for all chords; you pick five strings at once for the C chord, for example, and only four for the D chord.
Some guitarists use their fingers to strum, but most use picks. As a beginner, you probably want to go with a pick and save your virgin fingers some grief. Once you've finished learning the major chords in this video, check out three minor chords on the next page.