Someone wanted me to get homeopathy treatment, so I looked into the subject a bit.
The theory:
'Like cures like'
As I understand it, healthy people were given high doses of a substance, like phosphorus, potassium or some toxin.
Then the symptoms they developed from these substances were documented. When a person with a disease has certain symptoms, these symptoms are compared to the 'induced from a substance' symptoms. Then you get treated with the substance that induced symptoms in healthy people that are similar to your disease symptoms.
But this substance is given in an extremely diluted form.
A possible mechanism:
So I think the idea behind this might be to get the body to produce an anti-reaction.
Someone might have high blood calcium for example. The body has certain ways of reacting to that.
High blood calcium lowers parathormone levels. Parathormone generally works to increase calcium with higher vitamin D activation, more calcium-/phosphate-resorption from the bones, more phosphorus excretion by the kidneys,.. So the lower parathormone doesn't raise calcium anymore.
High blood calcium also causes an increase in calcitonin. Calcitonin acts to lower blood calcium by reducing calcium resorption from the bones and excreting more calcium via kidneys.
So the body has mechanisms in place to counteract/react to too high or low levels of certain substances. I could imagine homeopathy tries to use this effect by giving in a very small dose of (example) calcium, which hopefully doesn't raise the calcium further, but stimulates the body's reaction system.
Vaccines might use a similar mechanism, stimulating a helpful immune response with a very small dose of a virus? (I don't know much about how vaccines work).
I don't know wether the body's other systems work that way though, reacting to a small amount of a substance with a positive counteraction. I don't have any personal experience with homeopathy either.
Also, I would avoid taking toxic substances, there might still be a difference taking a mineral the body normally works with or a toxin. I wouldn't expect the effect to go as far as to cure ME/CFS, maybe it can influence certain symptoms positively.