The most important resource for English spelling is a good dictionary. Which dictionary should you use? A variety of dictionaries is available, suitable for various skill levels and specializations, for both British and American English.
For both British and American English, the Oxford English Dictionary is an excellent standard. For any word in contemporary English, it provides both British and American spellings. It is accessible online at www.oed.com (subscription required). Many schools, libraries, and universities have a subscription to the OED, and most state libraries will offer a free subscription via your library card - ask at your local library for more information. If you’d like a smaller, more introductory dictionary, the Oxford Advanced Learner’s Dictionary is an excellent choice for British English, and the Oxford Advanced American Dictionary is a great choice for American English.
For a more theoretical take on the inner mechanics of English spelling, Edward Carney’s A Survey of English Spelling is the classic tome on the subject. For a shorter take on the same material, consider Carney’s condensed version, English Spelling.
If you’d like to learn more about the history of English spelling, the Oxford English Dictionary is, again, an extraordinary resource. Alternatively, you could try a book on the history of the English language: there are many good options, but one recommended title is Brinton and Arnovick’s The English Language: A Linguistic History.