Here's a very well known song that is good for beginners to learn. The whole song is just one chord sequence constantly repeated. We've shortened the length because of that.
Just cycle through the following chord progression:
A minor - F major - C major - G major
These are each very common guitar chords and you need to learn how to play them!
Notice that between each chord there is a single palm muted strum. No matter which chord you are currently on, just flatten your fingers across the strings to mute them, then strum once (palm muted). The idea is to bring the strings to a dead stop. If you are unsure about the muting technique, check out the Core Skills section on Muting.
You don't have to use thumb-muting, as we show here. However it will make overall string control much easier.
Practicing a song like this will help you get the hang of learning to change between chords more smoothly and on time. Stick at it. The highly repetitive nature of the chord cycle will help you. Go slowly at it, and get it right, then build speed last. Play along with the slower ActionTab animation when you are ready (loop it). Once you can do that, start speeding up until you can keep up with the normal speed audio.
It takes time for your fingers to develop strength and dexterity. Doing repetitive chord changes is a great way to help those fingers get accustomed to the chord shapes and shifting between them quickly. It is painful work at first, but the more you work at it, the more natural it becomes. Don't wuss out on the practice!