The gold standard is first-person information, and this generally means conducting interviews if your subject is still within living memory. This in turn means tracking down people connected to your subject and reasonably likely to have relevant information. The best way to do this? Make use of the friend/acquaintance networks you already have. Let your friends/followers in normal life and on social media know who you're trying to contact and why. Chances are, a friend or acquaintance who shares your interests will be able to help you link up. Also, don't overlook personal websites. Not everyone has one, but if one is available, you may be able to make direct contact. If the person you want to interview is an owner or breeder, you may also be able to get access through their farm's website.
For active trainers and jockeys, if you can find out where they are currently plying their trade, you can write to them directly, addressing your letter "care of" the track. (Tracks' mailing addresses are usually provided on their websites.) Be sure your letter is courteous and to the point about the reason you would like to make contact, and provide multiple means of contact for the person's convenience (email, text, phone). Not everyone will respond to such a request, but a surprising number will.
Still stumped? If you have information regarding a possible third-party contact---perhaps a publisher or a professional/social organization that your hoped-for interviewee belongs to---you can try contacting the third party via letter or email. Don't expect the third party to give out the person's contact information; instead, ask politely if they can pass on your request. As always, be sure that your own contact information is clearly stated.
Personal letters, journals, and original photographs are also valuable first-person sources, especially when your subject is too far back in time for an interview to be possible. If you are able to contact family members or close friends of the person whose input you're interested in, they may be able to allow you access to such mementos, as well as possibly providing interesting secondary-source material. Other possible repositories for this type of material include museums, libraries, historical societies, and genealogical societies.
Newspapers and periodicals are the most popular secondary-source material, and fortunately, many web-based articles and a number of large Internet archives are available today, making it possible to do a lot of research from the comfort of your home. (My own favorite for digging beyond what Google or Bing will come up with is Newspapers.com, which is rapidly approaching the 1-billion mark on the total number of newspaper pages it has in its digital archives.) Some of these databases are free-access, but the largest ones require subscription fees. Still, compared to the hours and money you'd spend trying to track down the sheer volume of information they have available, they're for the most part quite reasonably priced. If a particular newspaper seems especially likely to have information on your subject and isn't in one of these broad-spectrum archives, you may want to contact the newspaper directly if it's still in existence and see if it has digital archives that can be accessed for a subscription fee.
Books, which represent information that has already been compiled from multiple sources and organized with a particular slant or target audience in mind, are a bit trickier as resources, but they can provide interesting information and their bibliographies may provide clues to further sources that you can use. Even if you live in Tinytown, USA, books may be more available than you might think. Interlibrary loan (check at your library's information desk) can help you access quite a few volumes that are out of your immediate reach, but be warned: if the book you want is old or rare, you may get only limited access (like being required to do your reading and note-taking in the library rather than being allowed to check the book out), or it may not be available at all because no library in the network will allow its copy to leave its own premises.
Finally, there are those sources that will require some legwork on your part but are invaluable. Tops among them for Thoroughbred lovers is the Keeneland Library in Lexington, which is an absolute treasure trove. While they're working on getting more of their holdings digitized and are very helpful in responding to long-distance requests, to get the best from them will require an actual site visit. It's well worth it. Among the treasures here are complete or nearly complete collections of the Daily Racing Form (both daily issues and chart books), the Blood-Horse, the Thoroughbred Record (later Thoroughbred Times), and the American Racing Manual series. Keeneland also has large picture collections by many noted equine photographers and copies of a large percentage of the books that have been published related to the Thoroughbred industry. The National Sporting Library and Museum in Middleburg, Virginia, is another one I've seen mentioned often as an extremely helpful resource, though I've never been able to visit it. Other possible sources? Consider state or regional breeding associations, museums related to the time period your subject lived in, historical societies, genealogical societies, and morgue files at a newspaper or periodical that hasn't gone digital. You may have to make arrangements in advance to be allowed access to some of these, but the results can be well worth it.
Happy hunting!