In my opinion the best way to get started with writing in Japanese is to learn to write hiragana and katakana properly. JPod101 has a very good video series called Kantan Kana here:
http://www.japanesepod101.com/index.php?cat=47. There are 25 short videos in the series: you can work through them and it's not at all difficult to learn the kana over a single weekend.
I'd recommend getting a pen and paper and following along with the videos--don't just sit there and watch them; write along with the presenter. Rewind and pause the video as much as you need to. There are five kana in each video, and it's a good idea to check that you can write the kana you've learned in the right order after each video--so five kana after the first one, ten after the second, fifteen after the third, and so on. Being able to write them in order will come in very useful in the future because sooner or later you'll decide you need a Japanese dictionary and, of course, the dictionary is going to be in the same 'alphabetical' order as you've been practising.
Once you've done the videos--and you really
can do them over a weekend--I found it was good idea to write the entire hiragana and katakana sets out once or twice a day, just to make sure I could do it (and you'll know for yourself when you don't need to do this any more). Once you can write the kana, reading them is a piece of cake: you won't get muddled up by the similar-looking ones because you know how to write them and can easily tell the difference between わ, れ and ね, ぬ and め, or ツ, シ, ン, ソ and ノ.
Now you can go back to the Lesson Notes and focus on the first section--the one with kanji and kana. You should have no trouble with the kana, but the kanji are a different story. You can start to tackle them by reading along while listening to the dialog audio (which will tell you how they are pronounced), or you can use the kana-only section as a crib. In addition, I like to write the kanji-and-kana text out (preferably on genkouyoushi, the squared Japanese writing paper) as I find it much easier to memorise kanji if I know how to write them. Again, writing helps to make it easier to tell the difference between similar kanji such as 持つ (
motsu, to hold) and 待つ (
matsu, to wait).
マイケル