You automatically have copyright on anything you write, be it your magnum opus or your shopping list. You don't have to claim or register them in any way. You wrote it, you own it. Your words could be sold in a variety of formats - hardback, paperback, audio, large print, digital, serialisation, film, condensed etc - and each of those formats could be sold to all the countries in the world.
Basically, what you are selling is the right to publish in a particular format in a particular territory for a particular period of time. Usually, so long as the book remains in print, the publisher retains the right to publish. If it falls out of print (deemed as the publisher having fewer than a certain number eg 250 copies in stock), after 6 months the author can ask for the rights back, and the publisher must hand them over.
At that point the rights could be sold again to another publisher, or the author could self-publish - there are quite a few authors with a back list of titles which have gone out of print, so the rights have reverted, who are busily putting them out as e-books.
If you are offered a deal by a Big 6 publishing house (ie the major international conglomerates such as Random House or Hachette - who own Headline, my publisher) the minimum they will ask for hardback and paperback rights in the home country. A smaller publisher may only publish in a single format, therefore they may only want the rights in that format - it used to be commonplace in the days before conglomeration for an author to have one publisher for hardback and another for paperback.
The publisher may also want the rights in other territories so, for example, USA publishers get Canada, UK gets Australia and New Zealand. I once had a deal almost founder because both my UK and my USA publishers wanted the rights to distribute the English language version in Europe. It was settled by the UK getting the EU countries, and the USA getting the non-EU countries.
If you have an agent, they usually retain the world rights in the hope that they can make deals with lots of different countries. Otherwise, you can sell the world rights to your publisher, and their rights department will do the selling in the same way an agent would. If you're selling a picture book, because of the expense of printing in full colour the publisher will expect to recoup the costs by selling around the world, and world rights usually go to the publisher as a matter of course.
Selling to a publisher in another country will mean a new contract and a new advance. The size of the advance will reflect the size of the country - Germany will pay a lot more than Norway, for example. This may not be ££££ but it all adds up.
In exactly the same way as the rights to different countries, audio and large print may be included within the publisher, or retained for sale by the agent to specialist publishers. Condensed books used to be published by Readers Digest. They printed awesome amounts of copies, and got huge discounts so the author got a few pence for each one. Book clubs were the same - high volume but at a high discount. This market used to be more important than it is now.
Nowadays, publishers are after the e rights as well. The standard deal being offered by print publishers is 25% of the royalties. A lot of authors think this is a poor percentage, given that the publishers aren't offering an advance or additional marketing for example, and the chair of the Society of Authors recently called for the % to be revised. It's worth pointing out that you don't HAVE to sell any of your rights - I've hung onto my e-rights, for various reasons. A specialist e-publisher usually gives a higher % of royalties.
Serialisation rights are relevant when the book is sold to a newspaper or magazine for them to publish extracts over several issues. It's less likely to happen with fiction, unless you are a publishing superstar. When you hear of a celebrity book being bought for £500,000 that's because the rights department of that publisher has already done a deal with a newspaper. Essentially, the newspaper is going to pay for the advance, rather than the publisher. So a celebrity book can sell only a few copies and still make money for the publisher because the advance and at least some of the publication costs have already been covered by the sale of the serialisation rights.
You can, of course, do it yourself, but it's in the rights selling that an agent earns their keep. Agents either have branches in different countries or, more usually, have agreements with agents based there. They're called co-agents. The commission is usually 20%, ie 10% for your agent, 10% for the co-agent. Quite a few agents have come from rights - my own agent, for example, used to run the rights dept of a Big 6 company. I'm pretty sure that my books are sold to so many countries (14) and in so many different formats because she's a demon at selling rights, rather than my writing having some fabulous global appeal. (I wish!)
How the money stacks up...each individual sale of rights is unlikely to be the stuff of your wildest dreams but they add up. I'm getting around £1000-2000 for most rights sales in different formats and the smaller countries, much more for the larger countries, and there is always the potential for royalties on top of the advance for each sale. It's very nice getting an unexpected royalty cheque from audio sales or Brazil, for example. The most rights sales I've had from a book is over 20 (doing a quick count in my head), the fewest about 5 - and that's all on top of my original advance from my publisher.
When you consider the potential for income within rights sales, it becomes clearer why most conventionally published authors are a bit arms length re e-publishing. An author's income isn't just about the basic deal, it's also about the sales of subsidiary rights. Include those in the equation and e-publishing doesn't look quite so wonderful in terms of income generation because it is only one format. I'm a teeny fish in the publishing pond - consider the subsidiary rights deals some of the big fish are getting...
Sorry, this has ended up as a long post, and I've still only touched the surface. I could have included a rant about Google misappropriating authors' rights, and it's worrying that so many people seem to think that authors only want to be read and don't want to be paid for their work and therefore won't mind when they help themselves to it (what authors usually call stealing).
The chances are you won't need to know much more about rights because your agent will do it all for you. But if you don't have an agent and you get offered a deal, read the small print carefully. The Society of Authors will check contracts, and that alone is worth the membership fee - and a whole lot cheaper than getting a lawyer to do it, plus their rights department has all the expertise.
Know what you are selling and don't passively hope it will turn out OK because you might not be doing yourself any favours. Don't forget - you have rights! Sell them, or hang on to them, the choice is yours.