Watch the Beside the Campfire online guitar lesson by TrueFire from Beginner Guitar Explorations
Lesson Source: Brad Carlton's Chord Studies: Beginner Chords Vol. 1
In this example, you'll be playing two chords: a C for one measure and an A Minor for one measure. Start by playing whole notes, or holding the chord for four beats on each chord. Once you've become comfortable with the change between chords, you can start to mix in some more picking hand patterns and rhythmic variation.
As far as the fingering is concerned, these two chords exhibit a very important fingering principle called "pivot fingers." That means that the same finger stays in the same fret on the same string when you change chords. Your first and second fingers in this example will work as pivot fingers. Don't worry if they shift slightly in the fret, but try not to remove them from their respective strings.