This book series is controversial - people either love it or hate it - but "Remembering the Kanji" by James Heisig is what I would recommend to start seriously studying kanji. I've worked with the first volume on and off, and when I was doing the exercises every day I could feel my grasp of kanji growing.
I know someone, a fellow American, who sat down and worked with Remembering the Kanji for six months straight, and now she can read almost anything in Japanese. I mean, she studied Japanese before that and knew the basics already, but RTK was what put her over the top for kanji comprehension.