Where do you find research studies on Homeopathy
Finding research on Homeopathy can be difficult. Even if you know which database to search in, the articles don't always mention the word homeopathy. Instead articles will investigate "highly diluted substances" or nanoparticles of different substances but the substance they are studying is really a homeopathic remedy.
You still need to read carefully however, since nanoparticle research and research of highly diluted substances are not always researching homeopathic remedies (I know, it can be so confusing). So when you search, you can search for the words homeopathic or homeopathy, but also try nanoparticles and high dilutions, but then read the results carefully to see if you have found what you are looking for.
When it comes to where to search, the first go-to is PubMed, a database of medical research papers. Any topic in medicine, homeopathy included, will usually be well represented in PubMed. Not all research is available in PubMed however. To try and remedy this, a few organizations have put together compilations of all homeopathic research. Iris Bell, a great homeopathy researcher, and Peter Gold, a Homeopath in New England and the Communications Director for NIH compiled "Homeopathy Research Evidence Base: References, 2017", a 200 page document on the different research studies on Homeopathy. This is a part of a project headed by the Canadian Academy of Homeopathy. The Homeopathy Research Institute (HRI) also has a database of research (although you have to create an account to access it - it's free though) and lists of external and internal publications that they have curated (meaning the results are biased - you will find mostly positive studies there). Their website has a lot of interesting information and is worth poking around if you are interested.
Old Homeopathic journals are also great places to look if you want to read cured cases. Archive.org has many old journals, such as the Hahnemannian Monthly, and old Homeopathy texts that are great reads if you are interested in history or philosophy.
If you are looking for broader knowledge on homeopathy, such as ethical arguments for and against it, you can look through SSRN. SSRN is similar to PubMed, but includes papers from a more diverse group of disciplines such as law, philosophy, women's studies, politics, marketing, business, etc.
Research studies are incredibly valuable in that we learn more about our remedies and homeopathic medicine in general, as well as (hopefully) increase the reputation of this medicine in general, in this era of "evidence based medicine". However homeopathy has hundreds of years of cured cases and hundreds of high quality studies (provings) on medicines, which is often not considered "evidence". I however believe that compilations of cured cases and drug studies are invaluable to the profession; practitioners need drug studies (provings) in order to treat their patients, and cured cases are evidence that the therapy works in real life. These types of evidence are found in Materia Medicas and old journals, as I mentioned above. Some materia medicas to read for good information on homeopathic remedies are Boenninghausen's Characteristics, Clarke's Dictionary, Hering's Guiding Symptoms (which includes some cured cases), and Allen's Keynotes.