The tricky part to playing by ear, is that sometimes there are places when you can stay on a chord, and other times when you can add extra chords, and it all sounds fine. It sounds different, but still right. So, when to change and what chord to change to can be variable. The genre of the song can be your guide. It is probably easiest to attempt folk songs first, since they often use a simple set of chords. Knowing when to change comes with practice, and with a 3 chord song you have a 50-50 chance of guessing the right chord. I just play a chord until it doesn't sound right, then search for the proper one. If you restrict your choices to the chords in the key you are playing in, it becomes a lot easier. For example, the key of C would use C, F, and G7: the key of F would use F, Bb, C7. If you can play with other people, it can help as well, because you can watch when they change, and start to develop your ear.
–Lori