[dba-SQLServer] Export / Import SQL Dbs

I'm currently at work on a project involving two SQL Server dbs that live
in a cloud. I have been granted access as admin to both. I want to extract
all the data from DataSource 1 and then perhaps do some mods due to
field-name conflicts or at least non-parallel names, and subsequently
import said extract into the new db.

This is new turf for me. Most of the time invested shall be unbillable,
since this is primarily an educational experience, although at least a few
hours shall be deemed billable.

If I had local copies of both Source and Target, then I could easily whip
up an SSIS ETL transform that would do the job, but I am unsure how to
handle the remote targets.

Anyone done this sort of task before? Any tips and hints to help me through
this?

-- 
Arthur