If I want to run this sort of query in SQL Server, how can I do the same query from one server I am connected to to another?
I tried adding \"[ServerName1].\" before
If you have adhoc distributed queries enabled you can use OPENDATASOURCE. Setting up a linked server is another option. Not sure of the pros and cons of each approach.
INSERT INTO [DatabaseName1].[dbo].[TableName]
SELECT FieldName
FROM OPENDATASOURCE('SQLNCLI',
'Data Source=Server\InstanceName;Integrated Security=SSPI')
.DatabaseName2.dbo.TableName