For the English speaker interested in learning to read Japanese , beyond a firm commitment to learning radicals and a high tolerance for feeling like an idiot, I recommend a system designed by Jack Halpern, and used exclusively in dictionaries for which he is the editor.

The best place to start is the quite reasonably priced "Kodansha Kanji Learner's Dictionary" (ISBN 4-7700-2335-9)

Designed for the English learner of Japanese, the dictionary does not assume that its user knows lots of radicals and their various pronunciations. Halpern's SKIP system organizes kanji first by general shape, then by stroke count. This produces a three-number code. Once you know the code, it becomes much less tedious to find the kanji you want. The dictionary gives pronunciations for kanji, in both Japanese and Chinese readings, stroke order diagrams, and several common usages. Halpern even considers that for many kanji it is easy to miscount the strokes. For such kanji he includes pointers to the correct stroke count.