you can use an ajax call coming into (for example) a php script on the server, which keeps the connection open and only replies if and when something needs to be displayed to the user. should nothing happen within a certain time, the connection gets closed and the client fires a new ajax call.
note that this only addresses the client/server communication, you would still need a notification method inside the server to wake up the php script if you want to avoid having a script constantly polling the database, but there are quite a lot of soultuions to this and they depend on what language you use on the server.
