Try to get fluent with your chord changes. The best way is to just play the chords one after the other in different order, or find a song that contains the chords you have just learnt. Between some chord changes there are finger numbers that remain the same, be aware of these chords as they will make chord changing faster. As you can see below in the 1st example, when you are changing from an A Major chord to a D Major chord, the first finger doesn't move from the 3rd string 2nd fret, this finger is called your pivot finger. Try and keep your finger down on the string when you are changing between these two chords.
Below is a diagram showing you how chords are usually written down. Roll your mouse over the diagram to help you with the naming of each part, then click to learn more about them if you are confused.
The 4 over the 4 represents 4/4 time, this means there are 4 beats per bar. The two vertical lines followed by two dots on the beginning and end are repeat signs. This means once you get to the end, play from the beginning of the chord progression again. Normally repeat signs only mean to repeat once, in this case repeat as many times as you need. The E A D & A represents each chord you should be strumming. The 1 2 3 4 under each one of those chords represents the beats in the bar. The vertical line in the middle is the bar line, this makes this chord progression two bars long.
Can you see how in the example below the first finger stays on the same string all the time, try not to lift it when changing frets just slide it. Once you can do these changes fluently we introduce strumming.
The red "V" pointing downwards represents a strum down. This means you're strumming from the thick string to the thin, try and strum fairly quickly, don't take too long to get from the thick string to the thick string. When you strum it should be a wall of sound and not racked over the strings.
= Strum Down (from the thick string to the thin)
Try and strum along with the example below. Count the beat when you are strumming, this is to help you keep in time. If possible try to tap your foot on every beat.
Another tip is to start changing to the next chord as soon as you've done the second strum. Try to keep the strumming fluent and in time.