On your server, you can setup IIS or Apache to be your web server software to host your HTML and Java site.
Next, you will have to think of a domain name and then see if anyone is currently using it. If not, then you will have to register it and pay a yearly fee to keep it registered.
Next, you will have to get a static IP address from your local ISP. You cannot have a Dynamic IP or no one will be able to find your website easily because of the changing IP address. You will also have to setup a DNS server. This is so that people can find your site.
What you could do is get a static IP address from your ISP for your DSL connection (it may cost you more). Then hook up a DSL router/firewall with 4 ports. then tell the router to direct all port 80 incoming traffic to the private IP of your webserver. You may also want to ask you ISP what is the Maximum bandwidth you can use per month. Since you will be hosting your own webserver, some ISPs will charge you alot of money if you have heavy traffic on your line and go over a certain amount of bandwidth per month.
Hope this has answered some of your questions.