This is a challenge that every historian/history enthusiast finds him/herself facing. Overall, there's no way to completely remove bias entirely, but when it comes down to it, there are two key avenues to approach it.

The first, is primarily research primary sources. For World War II, this would include listening to written or recorded speeches, after action reports of battles, videos or photographs, old news paper articles (although this can often fall into secondary source material) etc. Sometimes this can be a challenge to start out with, that's why any accredited university will provide it's students and faculty with access to online research data bases which allow students to find much of this information first hand.

The second way is to read "academic" or "scholarly" books by well-known or well-established historians. Now these are different books from "popular" history books, like Band of Brothers. Rather, a book like Why the Allies Won by Richard Overy is much more analytical and in-depth.

But then you'll probably wonder how does that Historian get to have his name up there with other great historians. Well, what ends up happening is that when a book like that is published, other historians in the field will write academic book reviews, which judge the material, the arguments, and if the book has any biases that are apparent. These will often be written in academic journals like The Past and Present which you probably don't have easy access too. However, many public libraries and most university libraries have access to these periodicals, and you can search for them this way.

I am not a World War II historian, so I apologize for not being able to be more specific with my resources. (I ended up pulling up my old notes from an American history class to find that book for you haha). But if you have any further questions, please let me know.

You shouldn't be afraid. You are correct that you will find biased information; no information isn't. Everything that is recorded is a product of its times and reflects the prevailing attitudes of the time and place it was recorded. That shouldn't discourage you, however. If you want to learn about World War II, there is plenty of information out there. Just pick a source and start reading. If something intrigues you, read up on that. The more you read, the more you will be able to establish a general sense of things and evaluate the veracity of different sources. Whatever you do, just keep reading and think intelligently.