It depends on how you like to learn. I, personally, hate learning from paper. I want a program on my screen telling me what to do and when. If you’re like that, I’d recommend a website called Wanikani. It’s a paid service, but the first three levels are free. I’ve nearly finished the third one and even that little amount has been so much help. The system works like this): “radicals” are taught. I put that in quotes because they’re not real radicals, nor do radicals mean anything in reality. But wanikani takes little pieces that appear in lots of kanji, calls them radicals, and gives them a meaning. These radical meanings have no real-world use, they’re only there to help with memorization. After learning the required radical pieces, the program proceeds to teach you actual kanji, and vocab using that kanji. Your memorization of the terms is tested through an SRS (spaced repetition system) algorithm.
Everything is memorized through story mnemonics. For example, 毛 is a kanji and is formed by the “radical” 彡 which wanikani says means “hair”. 毛 is hair with a tail attached, almost like an animal. Except animals have what we call -fur-. So, 毛 means fur, as in, animal hair. But there’s so much fur! You have to -mow- it down. Mow sounds just like “mou”, the pronunciation of 毛.
That’s just one example. A little strange, no? But that’s the point, the weirder the story to remember it is, the better you remember it.
And this is how I’d recommend learning kanji/hanzi/any character based writing, with or without wanikani. Separate the characters into smaller pieces, and make up stories to remember what they all mean and how to pronounce them.
In fact, it looks like,“The Kodansha Kanji Learner’s Course” (I believe that’s the book you got) teaches in a very similar way, so definitely give a solid effort to use that book. If you prefer programs, try out wanikani and if you like books, you’ve already got an excellent one to use!
Additionally, like it’s been said here, I’d also recommend SRS systems like Anki, and the reading material here can only help you 
About Anki, I’m probably in the minority in here, but I try to keep my decks to only 200-300 cards. I’ve seen decks with over a 1,000 cards, and this guarantees that you’ll get the max limit of cards to study every day in that deck for a VERY long time, giving yourself a bigger work load compared to, say, four 250 card decks.
Lastly, I use a site called duolingo, it’s like Rosetta Stone but entirely free. BUT, there’s no option for English speakers to learn Japanese, so I’m registered as a Japanese speaker learning English. It’s helpful for learning new vocab and to practise typing full Japanese sentences. You can use it everyday to keep your kanji in use and viewed in context! Beware though, the lack of any English help makes the grammar very hard to grasp… it does for me at least.
I’m still learning kanji myself, obviously, and I can only speak for what’s worked for me. I can’t speak as a veteran who already learned it all, but hopefully some of what I said is helpful ^^’
