How do I write and publish my own novel?
That's easy — just start writing!
But if only it were so simple. . . . Usually, when you begin writing a novel, you have in mind something you want to write about. Some authors start out wanting to address a particular issue that they care about; others have a story that they're dying to tell. Some authors may have a few characters that they like, and they just start writing about those characters — content to find the story along the way. And other authors will outline every single plot point of a novel before they put a single word of prose on paper. The point is, there's no clear-cut way to begin writing a novel.
Now, publishing your novel — that's another story (so to speak). Most legitimate publishers accept manuscripts only from authors with literary agents; however, the catch-22 is that most agents take on only published authors as clients. Then, how do you get an agent? The best way is to start small — write short stories and send them to smaller literary magazines. If your writing is good, you'll pick up some publishing credentials that will make getting an agent a little easier.
A word of warning: Don't be in such a hurry to get published that you end up paying a "vanity publisher" to publish your novel for you. Vanity publishers are not considered legitimate publishers, and paying a vanity publisher to publish your work will hurt your writing reputation.