"Learn to Write Chinese Characters" by Johan Bjorksten is the single best book I have ever seen for this kind of thing. It's about Chinese, not Japanese, and it doesn't have any practice drills or anything like that. What it is is a short, clearly-written guide to how characters work. It's good for quickly getting a feeling for stroke order, direction, and number. It also has a list of some of the most common radicals. I'd recommend reading this book (which should only take a couple of hours) and then just using the multi-radical lookup on WWWJDIC as much as possible.

I think it's better to learn kana and some basic Japanese grammar first to make sure you like it, before learning the radicals. The radicals are best approached later, when you can already read some Japanese.

Although learning the radicals first may seem to be the best approach, I don't think it's worthwhile until you have decided that you really, really want to learn Japanese. If you're not certain, it's too much trouble and you'll probably be frustrated more than anything.

For that reason, I recommend using one of the excellent traditional kanji dictionaries for learning the radicals- but, these all require proficient Japanese.

Also, most decent (older) Japanese textbooks will have the radicals explained in them.

Cheers,
Kaeru