Try memorizing a few kanji at a time, I suggest starting with Kyouiku Kanji. Learn the stroke order (which is actually relatively easy since it seems the stroke order always has a few basic, easy-to-follow rules that are impossible for me to explain and just easier to watch), and then just write those kanji repeatedly. You'll get them hammered into your head through repetition, and they'll stay there as long as you use them often enough.
It's easy to learn "compound words", too. Same technique, but first you have to know all the separate kanji. Then try writing down the actual characters together, keeping in mind the reading/s and meaning/s. You can use the same technique for kana.
Oh, and remember to quiz yourself, or at least somehow refresh your brain and reinforce what you've learned... Like writing them down again, going to random websites and pointing out the kanji and kana you've learned (Oooh, I know what this says! Kitty...) , or somehow getting Japanese books, preferably children's books. Workbooks are nice, too, if you can find them.
Perhaps not the best way to learn Japanese, and I've never had a professional teacher (definitely don't have the time or money to find a local one), but that's how I like to learn it independantly. When I have the time.