How do I make objects stick to moving platforms?

can you tell me exactly how to do that?

Try something like this in your Ball code:

 private void OnCollisionEnter(Collision c)
 {
     if(c.transform.name == "Platform")
     {
         transform.parent = c.transform;
     }
 }

Now you can do the reverse for OnCollisionExit to unparent the Ball again. This code also assumes that your platforms name is "Platform".

Also I would recommend reading up on the Unity Manual on Physics and Colliders:

i just got a bunch of errors from doing that

@GameVortex posted C# and it looks like you are using UnityScript..

 function OnCollisionEnter(c : Collision) {
     if(c.transform.name == "Platform")
     {
         transform.parent = c.transform;
     }
 }

now my ball is changing its shape, all weird, when it touches the platform

Picture