This is a real homeopathic remedy: Natrium Muriaticum -table salt- 30 CH, that is, with 30 dillutions of a hundred times each, so that's 10^60 of dillution. It says it's net 30mL.

Assuming this dillution is mass/volume, then there are 10^60 mL of water for every gram of NaCl. For 30 mL of water, that's 3 x 10^-59 g of salt.

In 58,44 g (1 mol) of NaCl there are 6,02 x 10^23 (Avogadro's number) "molecules". Not real molecules because it's a crystal, but you get it; since it's in aqueous solution there's this number of sodium ions and an equal number of chlorine ones. 
Therefore in 3 x 10^-59 g there are 3,09 x 10^-37 sodium ions.

But there's no such thing as 3,09 x 10^-37 of an ion or atom or molecule. It's 0, 1, 2, 3, 500 trillion or so on. 
Sodium chloride was split in Na+ and Cl- the moment it was dissolved in water, but afterwards its constituent ions remained intact through the whole dillution process.
Maybe I had a wrong supposition or calculation mistake but any conceivable way to model this still shows an absurdly tiny result.

So what can we conclude? There's a very small chance some stray ion found its way into Natrium Muriaticum 30 CH. But it's safe to say there's none of it. 
Zero. Nothing.
"Natrium Muriaticum 30 CH" literally is just water without any table salt at all. This is the case for most homeopathic medicines. Some are just concentrated enough to have a handful of molecules of their claimed source, but above 12 C they're arithmethically just water. There is no discussing this.

You can distill this remedy to examine residue. You can run it through any kind of emission or absortion spectroscopy. Any expensive method in analitical chemistry. In any case all that you'll find are trace impurities.
When you buy this you're buying overpriced water.

If A=B, B=A. Homeopathy is water, therefore water is homeopathy. Every glass of water you drink is nearly every single kind of homeopathic remedy that ever existed, exists or will exist. Likewise, every homeopathic remedy you purchase is not only itself but is also a thousand other remedies at once. Why pay for homeopathy? You already consume several liters of extremely potent homeopathic remedies every single day.

Hahnemann was blissfully aware of the Avogadro constant and other complications. His successors are either bydlo consumers who are too ignorant to know it or "specialists" who are content with a handful of half-assed explanations that have not been fully developed and all have conclusive rebuttals from real medicine.
What is the theoretical basis for the law of infinitesimals and similia similibus curantur? Can they be proven as hard laws? Remedies consist of pure water that was in contact with a handful of molecules two dozen dillutions ago, what biochemical mechanism makes them effective?

Homeopaths can articulate some technobabble on water memory and the like but they know that's no answer. They don't care. They believe in their quackery, firstly because they trust Hahnemann and secondly because of some empirical evidence. Just some, because there's more and better evidence against it.
Science is based not on crude empiricism but on developing theoretical models to explain empirical evidence. Homeopaths have weak empirical evidence, no model to explain it and no initiative to come up with a proper one. That places them in the realm of iridology, reflexology, Ayurveda and so on. It's a fraud. Only shithole countries like Brazil and India finance it.

The one good thing in homeopathy is its personalized treatments increase patient morale. But building an entire field of lies and LARPing just to smooth patient feelings is unethical.