There's really nothing to worry about -- Everyone learns things at their own pace. It not only has to do with the will and drive to learn something you're interested in, but it largely has to do with what sorts of resources you have at hand. Anyone can simply sit down and stare at a kana chart and try to memorize it on their own, but I'd bet that 9 times out of 10, it's nowhere near as effective as a learning program which was designed to help you retain the information.
When I first started learning my kana, I tried learning random Japanese words such as titles to Japanese songs. This was really ineffective because I was all over the place -- I didn't learn the kana in any particular order, and it messed me up. As for learning how to
write the kana, go one column at a time. For example, try to learn か、き、く、け and こ in one day, and take as many days as you need to practice them until you've got them down. Then move onto さ、し、す、せ、そ, and so on. Go a column at a time. By the time you've learned the entire syllabary, you should be able to write them out in order from memory without even thinking about it. I've fallen way behind on my Japanese practice, but I still take the time to write out both syllabaries a couple times a week to keep it fresh in the mind.
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Before you do anything else, though, try this: Go to
[this kana-learning website] and start with either hiragana or katakana
drag and drop games (I'd recommend the former). It may be incredibly frustrating at first, and you might have to just blindly guess where to drop many of the kana to begin with, but DO NOT give up. Play as many times as you can bear, and you'll be able to recognize every single kana from memory by the end of the day. I'd suggest doing this before trying to learn to write them. Once you've learned all of the kana and you can recognize them easily, try playing even more, but aim to get a better score by doing it faster every time. In my experience, I'd have to say that this was the most effective way to learn kana. It works unbelievably fast, so aiming to learn all of them in a day or two isn't an unrealistic goal as long as you're willing to fight through the inevitable headache and keep playing it over and over again.
I hope this helps!