Let's Begin: Katakana
In every way, katakana mirrors hiragana: for every hiragana character, there's a corresponding katakana character. Today, katakana is used for foreign loan words (like manager, computer, and microprocessor), foreign names (Clinton, Babe Ruth), and occasionally, for funky attention-getting, ala italics in English. (Note, there's a useful page that also shows you stroke order for this, see it here.)
Let's start with the first katakana:
I said it was boxy, didn't I? Nice and male. You can just picture Sen-no-Rikyu, the 16th century monk who invented the tea ceremony, writing verse with the above character.
The first five katakana are:
Katakana came into being after the creation of hiragana, the "woman's script": up until World War II, it was generally viewed as the "man's syllaberry" and was used by men, where women were supposed to use the "feminine" hiragana. After World War II, a social movement known as the Nihongo Touitsu Undou swept through the nation, effectively standardizing hiragana as the "base" kana of Japanese, and katakana as the kana to use for foreign words.
Katakana is set up the same as hiragana, with the same features: adding two little quote-marks or a circle to some of the lines changes the pronunciation (HA into BA, and so on), and there are "pairs" of kana that allow you to express words like JA, JU, JO, KYA, KYU, KYO, and so on.
Here is the whole Katakana list:
And the ga-za-da-ba-pa group:
Here are some foreign words that are written in katakana:
These are, from the top, coffee (the line, in case you didn't guess already, means that you're supposed to extend the previous vowel), banana, ice cream, jet (as in jet airplane), and Playstation. Pronounce them KOH-hee, banana (no intonation at all), AISU-kuRImu, JE-tto, and puREH-suTEHshon.
The third character in the word Jet, above, is a special one: it's called the "small tsu" and basically is a glottal stop -- that is, a tiny "stop" in the middle of a word, that allows for many more foreign words to be pronounced. It's also present in normal Japanese words sometimes, although I didn't cover it in the last section. It's expressed in roman characters with a double consonant (i.e., the double 't' in 'jetto'). It takes a while for you develop a "sense" of how to convert English words into their katakana equivalents, but it will eventually come to you.
Japanese is great for English speakers to learn in one sense because there are so many foreign loan words in use -- I mean, how many other languages use English words like "microprocessor" "memory" "gin and tonic" "sporty panty liner" and so on, in their present forms?