Studies show that homeopathic remedies work no better than placebo, but the placebo effect is a really powerful thing! It's actually thought that the effectiveness of antidepressants is mostly down to the placebo effect.
Alternative medicine can genuinely be helpful, but not because the actual treatments have any physiological benefit. Just having someone listen to you, care for you and assure you that they're doing something/giving you something that will make you feel better really does help the healing process.
We can also think about regression to the mean - if someone is ill, they often just get better on their own. If they take a homeopathic treatment, it'll seem like the treatment was effective, but really their body may just have healed itself anyway.
My feelings on homeopathy are somewhat complicated. Treatments that theoretically should have no physiological benefit really can be helpful, but I'm uncomfortable with all the dishonesty surrounding alternative medicine. I certainly wouldn't want severely ill people to opt for homeopathic remedies instead of evidence-based medicine.