Replicating an Install

I have a site which I would like to replicate on another domain. I want all of the files and plugin, db, etc. Then I will change some things on the new domain and sql and change the site. What is the best way to do this?

I just tried downloading the .sql file, uploading it to a new db and then coping over the files from the server to the new domain. I almost blew up my site! The old site started referencing the new domain even though I made no changes.

Does anyone have a good process to guide me through this? I appreciate the help!

Thanks,

Jon