I also found repetition and drilling the most effective for hiragana and katakana. It only took about 3 weeks to learn, and probably another 3 or 4 to "master" them.
My method was drilling by column. I started with the hiragana vowels a,i,u,e,o. Wrote them several times on their own, then in a column. The next day, I did sa,shi,su,se,so, writing them on their own, then i did the vowel and s columns, to redrill the previous day. Every day I added a column until I could complete the whole chart from memory. Not only could I read, but I could write. Same method was used for katakana. Start with one column and keep adding one a day, but always write the previous columns.
Then, once a week, I printed off blank charts for hiragana and katakana and filled them in, to see how much I retained. There were always a few that I would forget, but I kept at it. It only took a few weeks to "master" them. I feel like I got a strong base, both in writing and reading.