Connecting to SQL Server for first time

I am trying to connect to SQL Server for first time.  I just downloaded the interface and have never used it before.  I have been googling for help for a few hours now.  I cannot find how to fill out the Connect to Server - SQL Server dialog box.  I am using a personal computer and have no idea what to put in the box "Server Name".  I have tried"." as one article stated.  I have also tried IP address.  It's ridiculous that I have not been able to find this answer after this many hours of trying to get in.  Can someone please help?  I am on a deadline to get an assignment completed.  This answer should be easily found in the MS Help documentation for SQL but it's not...