You do not have to work in a library very long before you are asked about the order of books in a reader's favorite series. Nor will it be long before the question of who writes the books featuring "this" character. With all of the books and all of the characters, it can be difficult of not impossible to know all of the answers. However, what is important is not to know all the answers, only where to find them.
What book is first/next in this series?
One of the best resources is from the United Kingdom. Fantastic Fiction is a great website
Wikipedia. Yes, the site has a negative reputation, but it is a wealth of information both for characters in popular fiction as well as series information. Wikipedia does tend to be less accurate on some series than others, but always worth trying when seeking identification of characters.
Other Avenues for Identifying Series Fiction
Amazon.com is a great resource for finding correct titles for patrons who misidentify them. The site is not great for finding the order of books easily or identifying characters. But, it is a useful tool for quickly finding books that are out of print and those that have not been published yet.
In order to make the most of the links, one possibility is to put them in a folder on the desktop of main desk and reference staff. In addition, share them with your patrons on the library's website and printed materials. Part of readers' advisory includes sharing not only our print materials but those electronic ones that are useful.
Libraries are fantastic at marketing their printed and audio collections, but the electronic collections are often overlooked in the marketing blasts. There are many other choices than the ones that I have named here. However, I chose these because they are easy to use, intuitive, and can find results fast.
Good luck and have fun with it!