Like with Like is the key to Homeopathy. We match the symptoms of the patient with a remedy that would cause those symptoms in a healthy person. If you have a cold, for example, what symptoms may you have, yes a runny nose, watery eyes. What substance may cause those symptoms in a healthy person? Think about what happens if you are chopping an onion, your eyes water, your nose might start to run, so an onion causes these symptoms in a healthy person. A Remedy homeopathically prepared from onion will treat those symptoms in someone who has a cold. Like with Like. The important word here is that it is a Homeopathic Remedy which is prepared from the onion, we are not talking about giving onion to treat a cold it is the Remedy that is made from onion.
Follow the Clues
So, to summarise, Homeopathic remedies work by following the symptoms your body is already producing and continuing to nudge the body in that direction towards cure. It does not suppress the symptoms you are already producing, instead a Homeopath sees these symptoms as clues, clues your body is sending out so that we can follow these clues to find the Remedy required to restore balance. See my post on Homeostasis which will develop this thought further.