In the virtual server you can compete in past contests as if they were just happening now! You will have access to the same problem descriptions. Your submissions will be checked against the same test vectors. The virtual contest will have exactly the same duration as the original one.
From your point of view, the contest will start the moment you log in. All information (submissions, rankings, clarifications) will be will be updated as it were during the actual contest. For instance, if the first submission (from a team competing in the contest) occurred 5 minutes after the contest start, then that submission will appear in your listings 5 minutes after you log in for the first time. If the actual contest lasted 5 hours then your virtual contest will end 5 hours after you first log in.
To join a virtual contest you must select it in virtual server login dialog, and then press the Register button. After registering you will receive you user name and password in your email box.