You start by researching literary agents and query those who represent the kind of book you have written. Follow their submission guidelines precisely. Each will have a different set of guidelines.
Step2
Once you have an agent (getting one can be a long and excruciating process; Persevere), the agent will work to sell your book to a publisher. If your book is really good or especially timely, there might be an auction, where multiple publishers bid for your book.
Step3
When a publisher acquires your book, you will get an advance (a small one, probably, unless you're a famous person). This is like a down payment on the royalties you'll earn. Your agent will get a small percentage of this. Once the book is on bookstore shelves (up to two years from when the publisher acquired it), you will get a percentage of the price of each book sold. It's a small amount per book, but all put together it can add up.
Step4
Like I said, it's a long process, and you'll face a lot of rejection--even the best authors were rejected more than once. But keep at it, query every agent who seems right for your book, and with luck and good timing, and a well-written book and cover letter, you will succeed.
Tips & Warnings
Remember to be patient and dont give up because you got rejected once, keep trying!