Despite the tag on your question, the answer is going to be highly language specific. There are also going to be wide range of solutions depending on how complex of a solution you are willing to implement and how flexible a result you are looking for.
On the one hand you can accomplish a lot in a very short period of time with something like Python's mechanize, but on the other hand, you can really get into the guts and have a lot of control by automating a browser using a COM object such as SHDocVw (Windows-only, of course).
Or, as LoveMeSomeCode suggested, you can really hit your head against the concrete and start forging POST requests, but good-luck figuring out what the server expects if is doing any front-end processing of the form data.
EDIT:
One more option, if you are looking for something that you can come up to speed on quickly, is to use a AutoIt's IE module, which basically provides a programmatic interface over an instance of Internet Explorer (its all COM in underneath, of course). Keep in mind that this will likely be the least supportable option you could choose. I have personally used this to produce proof-of-concept automation suites that were then migrated to a more robust C# implementation where I handled the COM calls myself.