After you learn the basics of hiragana and katakana, you need practice! Practicing individual characters is useful, but being able to read kana fluently means reading whole words, almost without thinking about it. This app collects a list of hiragana and katakana words. When a random word appears, input the romaji equivalent in the text box and press enter. If you're correct, it will go on to the next random word, otherwise, it will let you try again. As a bonus, it also displays the meanings of the words, so you can also pickup the words' meanings as you go!
(I know some of these have kanji that are used instead of kana, but the focus of this app is to make reading kana as easy as reading the english alphabet, not becoming a fluent japanese reader)
For practicing individual kana, I'd recommend real kana.