Depends.
If you want to post the exact input of a form you have on your site (that is, you just replicate a form the other site has), then just set the form's action to the URL you want to post to and the browser will do everything for you.
If however you want to post some values you generate on the server (perhaps based on the input from your form), I'm afraid it's not possible. You can't redirect using a POST. Redirect is GET by it's nature.
BUT you might be able to fake it by doing a POST (using something like System.Net.WebClient) and then a redirect (it depends on how the other site handles the GET - it might display the same thing that it did on the POST, or not).
One more option (for the second case) would be to to do an AJAX call to your server, which will compute the required values, then do the POST to the other server from Javascript.