How to add a linked server to a sql server management studio?
Linked Servers are not database specific, but provide a pipeline between two servers.  Of course, the rights granted to the users will control which databases they can access.  The account you are using naturally needs to be able to logon to both servers with enough permissions to execute your query.

Yes, creating a Linked Server is an administrative function and not available to all.  Doing it yourself requires the ALTER ANY LINKED SERVER permission.

The parameters for the sp_addlinkedserver stored procedure are found at: http://msdn.microsoft.com/en-us/library/ms190479(v=sql.110).aspx

Also, under that link are instructions for several different ways to connect the servers together.  If Server X and Server A are both SQL Servers, the setup is quite simple.

You can use sp_addlinkedsrvlogin to manage how the logins authenticate across the linked server.   The details are at: http://msdn.microsoft.com/en-us/library/ms189811(v=sql.110).aspx 

Depending on your landscape and if you are using Windows Logins, you may need to have Kerberos configured properly on your landscape so that the Kerberos ticket (allowed permissions) can be forward to the other server.  See: Configuring Linked Servers for Delegation:

http://technet.microsoft.com/en-us/library/ms189580(v=sql.105).aspx