Maybe I'm late for the party, but I found the following links for me:
To execute the internal link, I used
EXEC sp_addlinkedserver @server='serverLinkPseudonym',@srvproduct='',@provider='SQLOLEDB', @datasrc='192.168.1.1';
Then, when I logged in with Windows Authentication, I added a Windows user (this caused a "Not Reliable SQL Server Connected" error)
EXEC sp_addlinkedsrvlogin 'serverLinkPseudonym', 'false', 'MACHINENAME\windowsLogin', 'lnkSrvLogin', 'lnkSrvPswd';
I also found that if I was going to run SQL Server Agent jobs that made LinkedServer calls, I had to add the following:
EXEC sp_addlinkedsrvlogin 'serverLinkPseudonym', 'false', 'NT AUTHORITY\SYSTEM', 'lnkSrvLogin', 'lnkSrvPswd';
For clarity: "192.168.1.1" is the IP address of the server you want to connect to. "lnkSrvLogin" is the login on the connected server that has access to the database that you need to access. "lnkSrvPswd" is the password for this account.
If you connect to a linked server using an account from an existing server, you simply use that account name in the sp_addlinkedsrvlogin command. eg:
EXEC sp_addlinkedsrvlogin 'serverLinkPseudonym', 'false', 'thisServerLogin', 'lnkSrvLogin', 'lnkSrvPswd';
Then check it out:
SELECT * FROM [serverLinkPseudonym].[DBName].[dbo].[TableName]