Word of warning: it's 10 MB, and pretty hard-core.
If you're writing a private app (as opposed to a public one), things are much simpler; you don't need all the OAuth stuff for starters. After a bit of trial and error, I got this to work:
To generate an API key and password, go to http://your-store.myshopify.com/admin/apps, and click "Create a private API key" at the bottom.