When learning to play open chords it can be extremely difficult and frustrating to attempt to play chords using 5 or 6 strings. Your fingers get in the way of each other and have not yet developed the coordination or the flexibility they need in order to cleanly play some of the larger, more spaced out chord shapes. Let's take a C major chord for example. The standard chord shape for C major involves 5 strings (5th through 1st). We can turn this chord into 3 smaller shapes that only use 3 strings: 3rd through first, 4th through 2nd, and 5th through 3rd. When you reduce the amount of strings being used in the chord, it allows you to use less fingers at a time which lowers the difficulty of the chord. In time you can then try using 4 out of the 5 strings, and eventually you will feel comfortable using all 5 strings. Smaller chord shapes also work great for getting used to the feeling of switching between 2 or more chords.
2. Fretting hand muscle memory
It is absolutely necessary to spend time developing muscle memory in your fretting hand. This is more easily done when you remove the strumming hand from the equation and focus on the fretting hand alone. The first step is to figure out exactly where each finger is going to be for any particular chord shape. Practice placing one finger at a time until you can place your fingers from memory. Next you'll want to practice hovering your fingers above the strings and forming the chord shape BEFORE you touch the strings. Once you have the shape, practice placing all of your fingers at once. Do both of these steps daily with all of your open chords and practice until you can change from chord to chord effortlessly.
3. Strumming hand timing
To begin, set up a metronome at 60 bpm. Practice a downward strumming motion and make sure it syncs up with each beat of the metronome. While attempting your downward strums, pay careful attention to the speed at which your hand comes back up for the next strum. The speed at which your hand comes up should be identical to the speed of your downward strum so that your hand is traveling at a consistent speed and never stops moving between strums. Once you have mastered this, practice adding in the upward strum. To do this, just get your downward strums in sync with the metronome and your hand moving at a consistent speed then simply allow the pick to hit the strings as your hand comes back up. If you are in perfect sync with the metronome, you will notice that the upward strum occurs exactly between each beat of the metronome. This method of combining a downward strum and an upward strum on each beat is the basis for forming simple strum patterns. I suggest exploring different combinations of upward and downward strums. Just remember to stay in time with the metronome. Once you feel comfortable strumming in time with the metronome, go ahead and try holding down a few chords with your fretting hand. The important thing to remember at this time is to keep your strumming hand in time, even if your fretting hand feels totally lost and keeps missing the chord shapes.