Dude, you got yourself some great teachers on here, Lol. When I first started with chords my hands wanted to die. I remember trying to play a C Major and go to D, and I kept hearing clicking and loud sounds. It just sounded horrid. Yes, your hands are going to hurt, and then you will notice your skin will begin to peel (Sounds fun... Lol).
But it is as simple as what the others have been saying. "Practice." There is going to be pain, heck there will be pain even when you are playing for many years. The better you get, the longer you play, the longer you play (In one day that is), the more you stress your hands. This is why most of us guitarist have faced tendonitis, carpal tunnel, and a series of other hand issues, including cutting our fingertips. Nothing is good in excess, so practice as much as possible, but remember to take periodic breaks.
If your fingers are really hurting, stop. If you have pain in your wrist, take a break for awhile. Do not push it, especially since I get the feeling you are just trying to become a rhythm player.
Lead players are the ones who tend to have to go an extra mile (But both can be equally complex in their own right).
So yeah, take your time. Patience is a virtue, man. You are going to hate the "barre" chords. Those will completely bust your playing hand up - I remember learning them and thinking "I will never be able to figure this out."
It takes time, patience, practice, dedication. Now I can switch between chords fairly quickly, and even I tend to lag at times. I think the basic F Major (Non-Barre chord) took me time to get use to switching back and forth with, I still am getting use to it. I never did use that often. But if you listen to my songs in my profile, I am playing it in "Break The Night With Colour."
Anyhow, good luck with this. You will be fine, just pay close attention to what these guys on here say, they are the experts (Seriously speaking).
Peace out, GuitarAnatomy.