It all starts with information. You begin the process by checking out other books in your genre. For this, you'll need your local library. Yes, you can check for books on your subject on Amazon if you are so inclined, but you'll still want to see physical copies of the books before you make your choices to see how each publisher handles the material and the layout. Go to the library (or bring their card catalogue up on line if they've gone high tech) and gather up an armful of books in your genre or on your topic. Check them out and see which publishers had an approach that is most to your liking. Go to the copyright page and get the full name of each publisher whose work you like. By taking this route, you've narrowed the field considerably before you take the next step.
Now, go back to the card catalogue and locate the most recent copy of the Writer's Marketplace that your library has. Look up each publisher who caught your eye. The Writer's Marketplace will give you a rundown on how each publisher operates and how they accept submissions. It will tell you if you need an agent to approach them. If not, it will tell you if the publisher accepts entire finished manuscripts or if they are looking for a proposal letter, an outline, and a few sample chapters instead. This is absolutely essential information as you do not want to waste your time contacting every publisher in the business hoping someone will like what you have written.
The most important step in this process, however, is to follow whatever steps the publisher asks you to take with great precision. Each publisher does things differently as each has developed a particular system that works best for them. Send them something that doesn't follow their guidelines and in most cases, your manuscript will be rejected. Why? Because your manuscript will take them more time than they are willing to spend on it if it doesn't conform to their guidelines.