Here's the way it works: When a book is submitted to Lightning Source (Ingram's POD printer), it automatically gets listed on iPage, the Ingram database.  This makes it available to most booksellers, both online and off.  Amazon is one of those booksellers who use the iPage database to update their own listings. It usually takes them a few weeks from the time the listing goes up on Ingram to get the listing onto their site.

Some publishers only set their books up on Amazon (for example, CreateSpace) and don't go through Ingram.  This means there will be a huge segment of the marketplace that will not be able to buy your book.  Most booksellers, online and off, use Ingram.

You can also set your book up yourself on Amazon, but be careful. Remember, POD books are more expensive to print than offset printed books, and as a rule, the discounts are lower. As an Amazon Associate, you may be expected to get less than you actually have to pay for your book.  It's usually best to let your publisher take care of this. If there's a problem getting cover art or other information onto your Amazon listing, your publisher should be able to take care of it.  Assuming your publisher is responsive, that is..