You don't have to be terribly gullible to fall for it. The human brain is not very good at statistics.
If you take something and then you feel better then it is natural to think that the thing that you did made you better. It could be the placebo effect. It could be that you were going to get better anyway.
I imagine that homeopaths are split between those who are actively conning people and those who are innocently (yet uselessly, and often harmfully) thinking that they really are helping.
It also seems that a lot of people on this thread don't understand what "placebo" means.