You've got a number of options. To expand on the answers from others and add a new idea...
Do it using the webbrowser control: This is technically possible by either injecting javascript into the target page as demonstrated here or creating a JavaScript object and using it as a bridge via the webbrowser.objectforscripting property. This is very fragile - something as simple as the website changing an element's Id could break it. You also need to make sure your code doesn't interfere with the functioning of the form (clashing function names, etc...)
Do it using a postback: Monitor the communications between the web browser and the server (I personally prefer Firfox/Firebug but ie/Fiddler or Chrome/F12 are both good too). As long as you can replicate the actions of the browser exactly, the server can't know the difference. The problem here is that browsers are complex and the more secure a form is, the more demanding servers are. This means you may have to fake a login, get cookies, send them back on subsequnt requests, Handle Viewstate data and xss prevention variables. It's possible and it's far more robust than the first option but can be a pain to get working. If it's not a highly secure form,, this is your best bet. More information here
Do it by browser automation: Selenium is probably the best option here (as mentioned by others) but suffers from a similar flaw to the webbrowser control in that it's sensitive to changes on the form itself (But not as mcuh so as the webbrowser control).
Incidentally, if you have Visual Studio Ultimate/Test edition (and some others, not sure which), it includes a suite of testing tools including an excellent engine to automate load testing a website. This is also superb for tracking down what exactly a form does as you can see every step of the emulation.
Hope this helps