The answer depends on how the website attempts to authenticate you:
- Do you have to set a username and password in the HTTP headers (basic auth)?
- Or do you have to fill out and submit a form containing the username and password?
For either I would recommend commons-httpclient, although the latter screen-scraping approach is always messy to do programatically.
For basic authentication, take a look at httpclient's Authentication Guide.
For forms authentication, you'll need to check the HTML source of the page to understand
- The URL the form is submitted to
- What the names of the parameters to submit are
For help on how to submit a form in httpclient, take a look at the documentation on the POST method.
The httpclient site also contains a basic tutorial.