To really learn how to play guitar you need to first learn how to make a transition between chords. A proper transition gives the song a sense of flowing, but a bad one can completely butcher the song, (yeas, its THAT Important). The next lesson in I play music will teach you how to play two strumming patterns while transitioning between chords. The main goal is to make the transitions seemingly effortlessly.
Is important to mention that transitioning between chords is a process and when you are a beginner is better if you start a out slowly. It doesn't matter how much you slow down at the beginning as long as you make the transition the right way . You can practice this by trying to play a few down strokes with the A chord and then switch to the G chord. Is important to have a constant rhythm as you transition between chords. You don't want to got too fast, is better if you slow down to ensure that you never skip a beat while strumming. The strumming has to be a constant and steady motion. With time and practice you will be able to speed your strumming but is a basic that you better grasp before you move on.
If you are wondering how to play guitar so that the transitions sound smooth and the song sound like it should, a good trick is to play some open high strings or muted strings as you make the transition from one chord to the other, that will assure you that the transition has a nice steady tempo or rhythm. When you play guitar keeping rhythm and tempo is very important. Try not to go really fast until you are comfortable with a slower tempo, then you can start speeding up.