It's actually really easy to publish a book on Amazon Kindle.
First, you need to create an account on Amazon Kindle Direct Publishing. Once you're logged in, you can click on the "Create a New Title" button on the right hand side.
Next, you'll need to fill out some information about your book, including the title, author, description, and keywords. Once you're finished with that, you can upload your book file. Amazon supports a variety of file formats, so you should be able to use the file type that you're most comfortable with.
Once your book is uploaded, you can set the price and choose whether or not you want to offer it for free. You can also choose to make it available for pre-order.
And that's it! Once you click the "Publish Your Kindle Book" button, your book will be live on Amazon Kindle within 24 hours.