The Katakana are what the Japanese use to write “foreign” words (to the Japanese). They can (and are) also used as/for “emphasis” (much like a “bold” font is utilized). For my student's purposes, the Katakana are “mostly” going to be used for writing “names” (usually of/for their students), and commonly upon “certificates” and such.
I usually show my student's the “Katakana” before showing them the “Hiragana”. This is mostly because it is rare for the average American to be writing anything in Japanese anyhow (and if they do, it's usually by way of “kanji”, rather than “Hiragana”).
The “use” of the Katakana, is purely “phonetic” (for “names”, and American “words”). The ability to “decipher” a person's name, takes a little practice, and a little experience with the accepted methods of translating those names when using the Katakana. I am going to provide a couple of “charts” I've made that I provide to my students (for this purpose).
The Katakana themselves, were derived from “pieces” of the kanji that their “sounds” came from. For my student's (and our purposes here) I'm don't get into that aspect of the “kana's” history.
The Standard “Katakana” Chart:
I am also providing a “Sound Change” chart which is used for various inflected, and “odd” (at least to the Japanese language) sounds.
Katakana Sound Change Chart:
(Click on Image to enlarge)