Depending on the student, I begin teaching in different ways. Sometimes, the best way for a student to get excited about learning is to practice the chords to one of their favorite songs. Other students learn better by starting with pick-holding and strumming technique. Some love to practice rhythm, others favor working on tone and pitch. Of course they all need to be taught, but introducing the basics should be as fun as possible.
Guitar lessons can be taught as early as age three, but I recommend starting with the 30 minute lesson for youngsters. Young students tend to have a slightly shorter attention span. I began learning the violin at age three, and it greatly influenced my aptitude and appreciation for music as an adult.