While HTTP is a pretty simple protocol in its most basic incarnation, building a browser as a client is very ambitious. Maybe start with the server-side and use an existing browser as the client. That way you don't have to worry whether the client or the server is the problem in case something doesn't work.
I assume you have worked through
http://docs.oracle.com/javase/tutorial/networking/index.html, especially the section on "All about Sockets", and gotten the client/server pair discussed there to work. If not, that should be the first step.
After that, read the HTTP specification to learn what an HTTP server needs to accept and respond to.