Katakana

/a/ - ア (underground)
/i/ - イ (i)
/u/ - ウ (cyrillic u - у)
/e/ - エ (i have an extra bone)
/o/ - オ

/ka/ - カ (similar to か) [ガ]
/ki/ - キ (key, similar to き) [ギ]
/ku/ - ク [グ]
/ke/ - ケ [ゲ] (it's a crooked "K")
/ko/ - コ [ゴ] (I have a cold)

/sa/ - サ [ザ] (Let socks dry)
/si (shi)/ - シ [ジ] (she has a crooked smile)
/su/ - ス [ズ] (my kid has a swing set)
/se/ - セ (similar to せ, серп і молот) [ゼ]
/so/ - ソ [ゾ] (a soy bean jumped out!)

/ta/ - タ [ダ] (titanic is sinking)
/ti/ (/chi/) - チ [ヂ]
/tu/ (/tsu/) - ツ [ヅ] (i have three peanuts)
/te/ - テ [デ] (a cat's tail)
/to/ - ト (tomahawk) [ド]

/na/ - ナ
/ni/ - ニ
/nu/ - ヌ (look at my new dress)
/ne/ - ネ (balancing is never easy)
/no/ - ノ (he has a long nose)

/ha/ - ハ [バ, パ] (ha, ha, ha!)
/hi/ - ヒ [ビ, ピ] (this is my heel)
/hu/ (/fu/) - フ [ブ, プ] (a hook on a wall)
/he/ - へ (same as in hiragana, a haystack) [ベ, ペ]
/ho/ - ホ [ボ, ポ] (I'm holding a holy cross)

/ma/ - マ
/mi/ - ミ
/mu/ - ム (moo-moo move!)
/me/ - メ (I mended my pants)
/mo/ - モ (similar to も: the more worms, the more fish)

/ya/ - ヤ (yacht)
/yu/ - ユ (a U-boa)
/yo/ - ヨ (Ё, I can yoga!)

/ra/ - ラ (рама велосипеда)
/ri/ - リ (similar to り)
/ru/ - ル
/re/ - レ (let's go)
/ro/ - ロ

/wa/ - ワ (a wine glass)
/wo/ (/o/) - ヲ (wow! He's happy!)
/nn/ - ン

Digraphs and diacritics

k -> g: カ /ka/ -> ガ /ga/
s -> z: サ /sa/ -> ザ /za/ (except ジ /ji/)
t -> d: タ /ta/ -> ダ /da/
h -> b: ハ /ha/ -> バ /ba/
h -> p: ハ /ha/ -> パ /pa/

u -> vu: ウ /u/ -> ヴ /vu/

?ャ ads /ja/ or /a/: キ /ki/ -> キャ /kya/
?ュ ads /yu/ or /u/: キ /ki/ -> キュ /kyu/
?ョ ads /yo/ or /o/: キ /ki/ -> キョ /kyo/

Links

Katakana on Wikipedia
Mnemonic katakana