Do you have an EFF TEE PEE (just trying to help!) program? I hear that FileZilla (Windows) is decent. http://sourceforge.net/projects/filezilla
1) Create a folder (on your desktop, or wherever) and call it MYSITE.
2) Use the FTP client to download everything into your MYSITE folder.
3) Use DreamHost Control Panel->Manage Domains to Add New Domain/Subdomain. Make sure it's Fully Hosted. Once this is created, take note of the Machine Name your site is on in the Manage Domains list.
4) Use the FTP client to upload everything from your MYSITE folder to 'machinename'.dreamhost.com and into the folder called 'yourdomain'.com ('machinename' and 'yourdomain' depend on your setup).
You don't need to transfer your registration, but you will need to go to your Registrar (GoDaddy, whatever) and update the DNS Servers to:
If you want to view your new site before the change:
1) Go to DreamHost's Control Panel->Manage Domains->Add New Domain/Subdomain
2) Create a Mirror Domain called 'mydomain'.dreamhosters.com and have it mirror 'mydomain'.com