Simple Task. It shouldn't take more than few minutes for someone who has worked on android phone book and web programming.
Create an android app that when opened will connect to the server and send entire address book. The server will store it. You can use xml or database to store it on the server.
Create a webpage on the server. When this webpage is accessed it will simple list/display the contacts that are sent by the phone and stored on the server.
There is also a Add button on the webpage. When clicked, allows user to add a new contact. Use minimum required fields like name and phone number only to add the contact. When user adds the contact on the web page, store it on the server in that xml/database and also send it to phone. To send it to phone, either the phone app can poll server every minute to check for any new contact or you may use push notifications.
Create an intent or something on android app that will listen to the newly added contact. When user adds new contact directly on the phone, upload that newly added contact to the server. When webpage is refreshed, it should include this newly added contact.
You may use any language/server of your choice i.e. asp.net/iis, apache, java, ruby etc.