How do I POST to a web page using Firebug?

AFAIK Firebug can't do this. However, there is a very useful Firefox extension, in the spirit of Firebug, called Tamper Data. This should be able to do what you want.

It allows you to monitor each request made by the browser, and you can turn on an option that allows you to look at, and edit, every single request before it gets sent.

Another simple solution is to load any webpage that uses jQuery, and type up a $.post() in the console.

Got here looking for a Firebug way of doing this. Then I realized that I could use Fiddler. This is the most powerful tool I know when it comes to debugging web requests.

Fiddler The free web debugging proxy for any browser, system or platform

Click the Composer tab and write your request as desired - then click Execute.