Paste the codes where? What you want to do is copy the HTML pages (index.html, etc) by downloading the files from one site (bravehost) and uploading them to the other (dreamhost).
Bravehost may have had templates that you were using? Dreamhost does not have that sort of system set up by default. FTP your actual page documents to the web readable area of your account, along with any image files, etc, and it should look fine. You could also upload a zip or tar of your entire site and then un-zip (or tar) it in place using the shell. This is a good way to transfer large sites with lots of sub directories and image files.