To save on the server you have two basic choices again, save to a full scale database, SQl Server, Oracle, Access etc. or just to a text file, maybe an XML file would be easier. Your decision depends on what software you have, how much data you intend to have (counting all users) and what you need to do with the data, is it just for the user or are you going to want to run reports and queries against it?
It seems like an overkill to use a database for just three names so an XML file might be easier.
As you are writing in .NET then it is simply a matter of checking, in the page load, whether this is a postback due to the save button being clicked or having an onclick on the save button. Then read the three values and construct an XML representation, something like:
<contact>George W. Bush</contact>
Load this into an XmlDocument using LoadXml method and then save to a file using the login name of the use, e.g., fawcettj.xml.
The next time the page is loaded check if the xml file exists and if so load and read the contacts to populate the textboxes.
Joe (Co-author Beginning XML, 3rd edition