You will need to start off your research by analyzing HTTP protocol side by side with the site you are using. A good tool for this task will be Wireshark, as it till allow you to watch the headers, POST and GET data, and COOKIES that get passed around.
After doing this, you will need to build your application to establish a TCP connection and emulate (intelligently) the way a user's web browser would.
Hope this helps (and you don't need SSL)
Motoma
I have tried Googling, but I can't find how to make a small browser application that goes to a website (specified by the user) and gets that page.
FlashGet and other download accelerators log in to the pages. I wondered how I could do it. I really need :). Thanks in advance.