How do we begin to learn how to play guitar chords? By learning your I IV V chord progression in the first position. In the key of C that would be C F G chords. If you need help, just do a web search for "chord progressions" or the "Nashville number system". Learn these chords in all keys. I do not mean learn them all right now but take it as a medium to long term task. Take a look at some sheet music or tabs for songs that you want to learn and work on the keys that your songs are in. That way you will be able to put your hard work to some good use.
If you have been working on how to play guitar chords while staying in rhythm you have probably found the going a little slow. The next step is to go looking for shortcuts. Sorry there are no shortcuts to fast chord changes, just slow, meticulous practice until one day you notice your body can change chords all by itself. Some people call it muscle memory, others say that all acquisition of motor skills is the work of "the intelligence of the body". Whatever the explanation, too much analysis never helps. What does help is repeated practice.
Learning chord progressions will train and strengthen your fingers and give you some practice in strumming. What is most important in this is to practice carefully so you are not repeating a whole lot of mistakes. What is at work here is muscle memory and the more careful you are to get things right, the faster will be your progress. The end result will be that the chord progressions will come automatically to you. This will stay with you all your life.
Another exercise for developing physical dexterity is practicing scales. One point that needs so be made here is to learn scale shapes. Just as there is an assortment of guitar chords in first position, and a few basic shapes that can be moved up the fretboard, there are also scale patterns that can be moved to all positions. One thing to look out for is the point where fatigue sets in after a few runs up and down the scale. Accuracy and speed do not necessarily follow warming up the fingers. The answer to this is do not spend too much time on scales if you do not yet know your chords. Once you know some open chords you can play a few songs which is something to show for your initial efforts. Then you can settle down to working on scales. Improvement in playing scales simply comes with some weeks and months of practice.
Once you have some basic chords under your belt, get yourself some songs like some basic blues or a few Bob Dylan songs. Play along with some CDs or whatever is on the radio. Your aim is to build your confidence and musical skill early in your career as a guitar player. This progress will help you in the next stages of learning to play the guitar.