There are several ways to do this. First, it depends whether you actually want Sun's
Java Web Server, or will any good
servlet and
JSP container do the job?
If you really need Sun's Java Web Server, your options are fairly limited. You can either:
1. Bet a permanent connection to the internet, and run the server on your box. This is expensive, and can need a lot of maintenance and system/network knowledge. Not really recommended unless you have access to a free/cheap high-bandwidth connection.
2. Buy or lease a "dedicated" server located in a shared data center. This is medium expensive (say $300-500/month) and requires some system admin experience, but most of the network issues are dealt with by the data center operators. You will need to install and maintain the Java Web Server and any other services you require yourself.
3. Lease some space on someone else's machine. There are a small number of hosting companies who claim to offer Java Web Server, but they are getting fewer all the time, and they are often the ones who don't keep up with technology, so I wouldn't be keen on using them,
If what you actually need is serve static files and run servlets and JSPs, then I recommend leasing some space with one of the many hosting companies who offer servlet/jsp support using one of the modern serevlet containers which support the latest version of the Servlet and JSP APIs. Look for Resin,
Tomcat, JRun, ServletExec and WAICoolRunner as high-profile and high-quality servlet servers, or Apache JServ as a good, although not quite up-to-date, alternative.