The first and easiest alphabet to learn is the KATAKANA alphabet. It is a phonetic alphabet for foreign words and names. Katakana is easy to learn and spot in Japanese because it almost always represents English words. It is basically used for "loanwords," foreign words which Japanese speakers incorporate into their everyday use. Japanese is full of these loanwords, and although most of them are taken from English, there are some that are taken from French, Spanish, German, etc...
Katakana is also used for proper names of foreign people, onomatopoeic words, and sound effects. Furthermore, if a writer wants to give a "special effect" to a Japanese word that already exists, he'll write it in Katakana instead of Hiragana.
So, without further ado, here's the Katakana alphabet. Look at it and study it, and then I'll describe how it works.
So, I guess the first thing you'll notice is that there's much more than the standard 26-odd letters of the Roman alphabet, won't you? Well, that's because all the characters in Katakana make up a single syllable and, with the exception of the 
character, form a complete sound. It would take two or more letters in our Roman alphabet -- a vowel and a consonant -- to make up most of the sounds of each of the characters in Katakana.
Secondly, Katakana is divided up into the five vowel sounds in Japanese: A I U E O. They are also divided up another way, into nine primary consonant sounds: K S T N H M R W N.
So, those are the basic building blocks of Katakana. It's easy to make some foreign words in Katakana. My name, for example, is 
, or "kurisu." My name is easy to make, because it uses just the standard characters. But it does get more complicated.
To add more sounds to Katakana, some consonants can become "voiced" by adding
two diacritical marks, `` and °. With the addition of `` after a character,
K becomes G, S becomes Z/J, T becomes D, H becomes B; and with the addition
of ° after the H-sounds, they become P-sounds. Basically, the unvoiced
sounds of the Katakana alphabet (ie: not using your vocal cords) become voiced.
So instead of KA SHI SU TO HI, etc... you'd have GA JI ZU DO PI, etc... Voiced
characters look like this: 
Double vowel sounds are easily represented as a dash: -. "Key," for instance, is 
, or "kii."
Double consonant sounds are represented by a small "tsu" symbol that doubles the following consonant. It's a little hard to explain, but easy to identify. For example, 
means "Rock" (RokKu), and 
means "Happy" (HapPii).
Two more things: By adding a small "ya" "yu" or "yo" after an I-vowel sound,
you can create a quick blend of the vowels. For example, 
reads as "Kya Ryu Nyo." You can also do this with all the vowel sounds; putting
a small vowel after a character creates sort of a diphthong-effect with the
two vowel sounds. This is evident in the title of the game "Valis": 
A few notes about pronunciation: First of all, I guess you noticed that a few sounds are missing from Katakana, most notably the L and F sounds. Well, when speaking Japanese, you need to pay attention to how you speak. You can't pronounce Japanese words as if they were English. The R sound is much softer than in English, and is halfway between a hard R and a hard L. So, that's where the L went in Japanese. "Hello" would be pronounced by a Japanese speaker as "Herro," but bear in mind that this is a very soft R sound. The F sound is incorporated into the H-line in a similar way. The H sound is not hard, nor is the F sound. Again, it is in-between the two. You'd pronounce the F/H as if you were blowing out a candle.
So, that's pretty much all there is to it. Now let's see if you can identify an actual game cover that's written in Katakana:
If you guessed "Doki Doki Panic," then you're right! Doki Doki Panic, for those of you who didn't know, was originally a Famicom Disk System game released by FCI. DDP never came out in North America, but it was translated into Super Mario Bros. 2 for release here! So, SMB2 as we know it wasn't originally a Mario game. DDP has an Arabian theme, and the four main characters that you can use to play are those pictured on the cover. Since it is a Disk System game, you can save your progress as you complete a level, and choose your starting level and character from a saved position. And you have to finish the game four times, once for each character, to get the "good" ending.
That's it for the Katakana lesson. Memorize those characters, and then head on to the Hiragana lesson!