iOS Submit form to a website, that is not mine?

It sounds like you would have to figure out the structure of the page that you want to post to. What do they use to post to it? Is it publicly available? Do they maybe have an API you could implement?

When a web form is submitted a POST or GET is generated in a certain format (application/x-www-form-urlencoded, or multipart/form-data).

All of the NSURLConnection wrappers have support for this. See AFNetworking and ASIHTTPRequest.

Also see:

http://en.wikipedia.org/wiki/Html_form