First identify the proper search terms. This can be:
- terms for spies and the organizations they work for: intelligence agency, secret service etc.; use a dictionary, thesaurus or encyclopedia (like Wikipedia) to identify more of these terms
- the names of these organizations: CIA, FBI, KGB etc.; use an encyclopedia to create a list of the organizations that are relevant for you
A good place to begin to get an overview of a topic is Wikipedia. You could begin at the articles for "Espionage" or "Intelligence Agency" and follow the links given on those pages. That will give you a first idea of the range of your topic, provide some first sources, and extend your list of search terms.
Next, search for books and documentary films about the work of "spies".
Use the terms and names you have identified in the first step to search in online bookstores (like Amazon) or in the catalogues of university and public libraries or in scholarly databases such as Google Scholar. There may be political, historical or even more specialized databases. Limit your search to the correct departments, if possible, such as history, politics, or biographies. Here is a screenshot of the departments I get recommended when I search for "secret service" on Amazon (look under "Books"):

As you find them, read the sources you have found. While you do so, note down new additional search terms or names or sources that are mentioned in those sources. Keep searching while you read.
Many writers contact and talk to professionals in the fields they want to depict, to ask them more specific questions. This can be the authors of the books you found or people who work in the organizations you have identified.
You may want to learn how to do academic research. There are books on this and many university libraries teach courses on how to do research. The courses in my uni library are open to the public.
Warning
As a writer, understand what your aim is and how much research you need to efficiently achieve that goal. Are you writing an action thriller and just need a bit of interesting information to make it feel authentic? Then don't spend months to become an expert on how intelligence agencies operate. Most of your readers won't know, nor care, because they are reading your book for the action.
Don't over-research.