I'm in the process of writing my very first book and I'd like to use the internet for research information. However, I don't want to do anything wrong. I realize I need to list the source of my info but do I also need to pay royalties to that source?
Almost never. Royalties apply to copyright, and copyright only applies to the literal text of the material. Anything you learn, you can use, so long as you don't use word-for-word quotations without attribution.
Let's say you are writing a book about Lincoln and you read Team Of Rivals (the source material for the recent Daniel Day Lewis movie Lincoln). You can use absolutely any fact, idea, or story from that book in your own, and you can even quote little snippets, so long as you put proper cites.
Incidentally, if you don't quote word-for-word, you are not under any legal obligation to cite or acknowledge your sources. However, it's considered good form, especially with a non-fiction book, to do so.
Adding to Malvolios answer, the prerequisite for your use of the information is that the information has been published and is publicly available.
You cannot use data that was given only to you and for a different purpose. E.g. if you pay a researcher or a research company such as Nielsen to provide data to help you decide a price and marketing strategy for your product, you cannot publish that information in your writing. In that case the owner of the data would need to grant you the right to publish their information.
If the information is public, you may use it. If it is from a copyrighted publication it is common practice and courteous to credit your source, even in fiction writing (add "acknowledgements" to the end of your novel or the end cedits of your movie).